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\newtheorem{defi}{D\'efinition}[section]\newtheorem{lemm}[defi]{Lemme}\newtheorem{prop}[defi]{Proposition}\newtheorem{coro}[defi]{Corollaire}\newtheorem{theo}[defi]{Th\'eor\`eme}\newtheorem{exo}{Exercice}
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$ [\,Q_{T_n}(\beta),Q_{T_n}(1-\alpha+\beta)\,]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4663}%
$ [\theta-\varepsilon , \theta+\varepsilon]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4677}%
$ n_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4685}%
$ \theta-\varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4691}%
$ Q_{T_n}(\beta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4693}%
$ \alpha\!-\!\beta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4695}%
$ n_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4703}%
$ \theta+\varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4705}%
$ 1\!-\!\alpha\!+\!\beta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4709}%
$ Q_{T_n}(1-\alpha+\beta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4733}%
$ 1-\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4735}%
$ \alpha>0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4745}%
$\displaystyle Q_{T''_n}(u) = \theta\,u^{1/n}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4749}%
$ \beta\leq \alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4751}%
$ [\,Q_{T''_n}(\beta),Q_{T''_n}(1-\alpha+\beta)\,]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4753}%
$\displaystyle \theta(1-\alpha+\beta)^{1/n}-\theta\beta^{1/n}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4757}%
$ \theta \alpha^{1/n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4761}%
$ \alpha^{1/n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4765}%
$ n\ddots \alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4785}%
$ {\cal B}(10,0.6)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4787}%
$ i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4789}%
$ F(i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4815}%
$ 1\!-\!\alpha=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4823}%
$ \mathbb{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4825}%
$ Q_T(1-\alpha+\beta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4827}%
$ 1+Q_T(1-\alpha+\beta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4829}%
$ \geq$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4852}%
$ \overline{X}_n=(X_1+\cdots+X_n)/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4863}%
$\displaystyle S^2_n = \frac{X_1^1+\cdots+X_n^2}{n} - \overline{X}_n^2\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4869}%
$ (X_1^2+\cdots+X_n^2)/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4871}%
$ \mathbb{E}[X^2]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4873}%
$ \overline{X}_n^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4875}%
$ (\mathbb{E}[X])^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4877}%
$ S^2_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4879}%
$ Var[X]=\mathbb{E}[X^2]-(\mathbb{E}[X])^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4882}%
$\displaystyle \mathbb{E}[S^2_n] = \frac{n-1}{n}Var[X]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4884}%
$ \mathbb{E}[\overline{X}^2_n]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4886}%
\begin{displaymath}
\begin{array}{ccc}
\mathbb{E}[\overline{X}_n^2]&=&\frac{1}{n^2}\mathbb{E}[(X_1+\cdots+X_n)^2]\\ 
&=&\frac{1}{n^2} 
\mathbb{E}\left[\sum_{i=1}^n X_i^2 + \sum_{i=1}^n\sum_{j\neq i} X_iX_j\right]\;.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4888}%
$ X_1,\ldots,X_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4890}%
$ \mathbb{E}[X_i^2]=\mathbb{E}[X^2]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4892}%
$ \mathbb{E}[X_iX_j]=(\mathbb{E}[X])^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4894}%
\begin{displaymath}
\begin{array}{ccc}
\mathbb{E}[\overline{X}^2_n]&=&\frac{1}{n^2} \Big( n\mathbb{E}[X^2] + n(n-1) 
(\mathbb{E}[X])^2)\Big)\\ 
&=&\frac{1}{n}\mathbb{E}[X^2] + \frac{n-1}{n} (\mathbb{E}[X])^2\;.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4896}%
\begin{displaymath}\begin{array}{ccc}
\mathbb{E}[S^2_n]&=&\frac{1}{n}\mathbb{E}[X_1^2+\cdots+X_n^2]-\frac{1}{n}\mathbb{E}[X^2] - 
\frac{n-1}{n} (\mathbb{E}[X])^2)\\ 
&=&\frac{n-1}{n}\mathbb{E}[X^2] - \frac{n-1}{n} (\mathbb{E}[X])^2)\\ 
&=&\frac{n-1}{n}Var[X]\;. 
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4903}%
$\displaystyle V_n = \frac{n}{n-1} S^2_n\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4905}%
$ \sqrt{S^2_n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4907}%
$ \sqrt{V_n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4913}%
$ \sqrt{Var[X]}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4917}%
$ \sigma_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4919}%
$ \sigma_{n-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4921}%
$ V_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4933}%
$ 6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4939}%
$ F_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4941}%
$ q=\alpha p + (1-\alpha)(1-p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4945}%
$ q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4947}%
$ \alpha=1/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4953}%
$ \alpha\neq$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4959}%
$\displaystyle p=\frac{q-1+\alpha}{2\alpha-1}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4963}%
$\displaystyle T_n=\frac{F_n-1+\alpha}{2\alpha-1}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4971}%
$\displaystyle \frac{q(1-q)}{n(2\alpha-1)^2} = \frac{p(1-p)}{n} + 
\frac{\alpha(1-\alpha)}{n(2\alpha-1)^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4981}%
$ \alpha=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4987}%
$ \alpha(1-\alpha)/(2\alpha-1)^2 = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4989}%
$ N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4991}%
$ m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5005}%
$ nm/N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5007}%
$ X/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5009}%
$ m/N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5013}%
$\displaystyle T=\frac{nm}{X}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5019}%
$ X+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5021}%
$\displaystyle T'=\frac{nm}{X+1}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5025}%
$ X'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5031}%
$\displaystyle T'' = \frac{nm}{X'}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5039}%
$ m=n=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5045}%
$ \mathbb{E}[T']$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5047}%
$ \sqrt{Var[T']}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5049}%
$ \mathbb{E}[T'']$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5051}%
$ \sqrt{Var[T'']}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5100}%
$ f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5110}%
$ f(X)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5114}%
$ \mathbb{E}[f(X)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5116}%
$ (f(X_1),\ldots,f(X_n))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5128}%
$ X-\mathbb{E}[X]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5130}%
$ \mathbb{E}[X^k]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5132}%
$ \mathbb{E}[(X-\mathbb{E}[X])^k]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5138}%
$ a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5140}%
$ \lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5142}%
$\displaystyle \mathbb{E}[X] = \frac{a}{\lambda}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5143}%
$\displaystyle \quad
Var[X] = \frac{a}{\lambda^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5151}%
$ Var[X]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5153}%
$\displaystyle a=\frac{\mathbb{E}[X]^2}{Var[X]}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5154}%
$\displaystyle \quad
\lambda=\frac{\mathbb{E}[X]}{Var[X]}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5162}%
$ \overline{X}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5164}%
$ S^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5174}%
$\displaystyle A=\frac{\overline{X}^2}{S^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5175}%
$\displaystyle \quad
\Lambda=\frac{\overline{X}}{S^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5181}%
$ b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5183}%
$\displaystyle \mathbb{E}[X] = \frac{a}{a+b}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5184}%
$\displaystyle \quad
Var[X] = \frac{a b}{(a+b)^2(a+b+1)}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5190}%
$ \mathbb{E}[X]=E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5192}%
$ Var[X]=V$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5194}%
$\displaystyle a=\frac{E(E-E^2-V)}{V}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5195}%
$\displaystyle \quad
b=\frac{E-2E^2+E^3-V+EV}{V}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5213}%
$ E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5215}%
$ V$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5227}%
$\displaystyle \mathbb{E}[X] = \frac{n(1-p)}{p}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5228}%
$\displaystyle \quad
Var[X] = \frac{n(1-p)}{p^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5238}%
$\displaystyle n=\frac{(\mathbb{E}[X])^2}{Var[X]-\mathbb{E}[X]}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5239}%
$\displaystyle \quad
p=\frac{\mathbb{E}[X]}{Var[X]}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5260}%
$ \widehat{P}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5264}%
$ 1/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5269}%
$ c_1,\ldots,c_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5271}%
$ x_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5273}%
$ h=1,\ldots,k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5275}%
$\displaystyle n_h = \sum_{i=1}^n$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5276}%
$\displaystyle _{c_h}(x_i)\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5278}%
$ c_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5282}%
$ \{c_1,\ldots,c_k\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5284}%
$\displaystyle \widehat{P}(c_h) = \frac{n_h}{n}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5287}%
$ \{c_1,\ldots,c_r\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5289}%
$ P=(P(c_h))\,,\;h=1,\ldots,r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5291}%
$ \widehat{P}=(\widehat{P}(c_h))\,,\;h=1,\ldots,r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5293}%
$ Q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5297}%
$ D_{\chi^2}(P,\widehat{P})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5299}%
$\displaystyle D_{\chi^2}(P,\widehat{P}) = \sum_{h=1}^r 
\frac{(P(c_h)-\widehat{P}(c_h))^2}{P(c_h)}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5303}%
$ \widehat{F}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5305}%
$ x_{(1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5307}%
$ i/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5309}%
$ x_{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5311}%
$ x_{(i+1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5313}%
$ x_{(n)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5318}%
$ F$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5328}%
$ D_{KS}(F,\widehat{F})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5330}%
$\displaystyle D_{KS}(F,\widehat{F}) = \max_{i=1,\ldots,n}\, 
\Big\{\,\Big|F(x_{(i)})-\frac{i}{n}\Big|\,,\,
\Big|F(x_{(i)})-\frac{i\!-\!1}{n}\Big|\,\Big\}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5344}%
$\displaystyle D_{\chi^2} = \frac{(f-p)^2}{p} + \frac{(1-f-1+p)^2}{1-p} 
= \frac{(f-p)^2}{p(1-p)}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5346}%
$ p=f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5353}%
$ Y_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5357}%
$ (x^{(1)}_i,\ldots,x^{(k)}_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5359}%
$ (x^{(1)},\ldots,x^{(k)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5361}%
$\displaystyle Y_i = f(x^{(1)}_i,\ldots,x^{(k)}_i)+E_i\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5363}%
$ (E_1,\ldots,E_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5369}%
$\displaystyle EQ(f) = \frac{1}{n} \sum_{i=1}^n (Y_i-f(x^{(1)}_i,\ldots,x^{(k)}_i))^2\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5373}%
$\displaystyle Y_i = ax_i+b+E_i\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5375}%
$\displaystyle EQ(a,b) = \frac{1}{n} \sum_{i=1}^n (Y_i-ax_i-b)^2\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5381}%
$ x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5383}%
$ Y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5393}%
$ \overline{x}=\frac{1}{n}\sum x_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5399}%
$ s^2_x=\frac{1}{n}\sum (x_i-\overline{x})^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5405}%
$ \overline{Y}=\frac{1}{n}\sum Y_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5411}%
$ S^2_Y=\frac{1}{n}\sum (Y_i-\overline{Y})^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5417}%
$ c_{xY} = \frac{1}{n}\sum (x_i-\overline{x})
(Y_i-\overline{Y})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5425}%
$ r_{xY} = \frac{c_{xY}}{\sqrt{s_x^2S_Y^2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5438}%
$ s_x^2\neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5442}%
$ EQ(a,b)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5444}%
$\displaystyle A = \frac{c_{xY}}{s_x^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5445}%
$\displaystyle \quad
B = \overline{Y} - A\overline{x}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5447}%
$\displaystyle EQ(A,B) = S_Y^2(1-r_{xY}^2)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5449}%
$ A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5451}%
$ B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5457}%
$ Y=(Y_1,\ldots,Y_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5461}%
$ {\cal N}(\mu,\sigma^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5463}%
$ \mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5465}%
$ \sigma^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5467}%
$ i=1,\ldots,n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5469}%
$ Y_{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5475}%
$ Q_{{\cal N}(\mu,\sigma^2)}(i/n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5481}%
$ {\cal N}(0,1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5483}%
$ Y=\sigma X+\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5489}%
$\displaystyle Q_{{\cal N}(\mu,\sigma^2)}(u) = \sigma Q_{{\cal N}(0,1)}(u) + \mu\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5491}%
$ x_i=Q_{{\cal N}(0,1)}(i/n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5497}%
$ (x_i,Y_{(i)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5499}%
$ y=\sigma x+\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5509}%
$ \sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5513}%
$ {\cal W}(a,\lambda)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5515}%
$\displaystyle Q_{{\cal W}(a,\lambda)}(u) = \left(-\frac{1}{\lambda} \log(1-u)\right)^{1/a}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5529}%
$ Q_{{\cal W}(a,\lambda)}(i/n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5531}%
$\displaystyle Y_{(i)}\approx\left(-\frac{1}{\lambda} \log(1-\frac{i}{n})\right)^{1/a}\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5533}%
$\displaystyle \log(Y_{(i)})\approx\frac{1}{a}\log\left(-\log(1-\frac{i}{n})\right)
+\frac{1}{a} \log\left(\frac{1}{\lambda}\right)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5535}%
$ x_i=\log(-\log(1-i/n))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5537}%
$ Y'_i = \log(Y_{(i)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5539}%
$ (x_i,Y'_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5541}%
$ y=(1/a)x+(1/a)\log(1/\lambda)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5547}%
$ Y'_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5551}%
$ 1/a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5553}%
$ (1/a)\log(1/\lambda)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5555}%
$ 1/A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5557}%
$ e^{-B/A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5574}%
$ p^6(1-p)^4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5580}%
$ 2.6\,10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5582}%
$ 1.8\,10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5584}%
$ 5.3\,10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5586}%
$ 9.8\,10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5588}%
$ 1.2\,10^{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5590}%
$ 9.5\,10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5592}%
$ 4.2\,10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5612}%
$ p=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5615}%
$ C=\{c_1,\ldots,c_k\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5617}%
$ \{P_\theta\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5619}%
$ C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5633}%
$\displaystyle L(x_1,\ldots,x_n,\theta) = \prod_{i=1}^n P_\theta(x_i)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5651}%
$\displaystyle \mathbb{P}[(X_1,\ldots,X_n)=(x_1,\ldots,x_n)] = L(x_1,\ldots,x_n,\theta)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5666}%
$ f_\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5680}%
$\displaystyle L(x_1,\ldots,x_n,\theta) = \prod_{i=1}^n f_\theta(x_i)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5686}%
$ \varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5694}%
\begin{displaymath}
\begin{array}{ccc}
\mathbb{P}\Big[X_1\in [x_1\!-\!\frac{\varepsilon}{2},x_1\!+\!\frac{\varepsilon}{2}]
\mbox{ et }\ldots\mbox{ et }
X_n\in [x_n-\frac{\varepsilon}{2},x_1+\frac{\varepsilon}{2}]\Big]&=&
\prod_{i=1}^n 
\int_{x_i-\frac{\varepsilon}{2}}^{x_i+\frac{\varepsilon}{2}} f_\theta(x)\,dx\\ 
&\simeq&
\prod_{i=1}^n f_\theta(x_i)\varepsilon\\ 
&=&
\varepsilon^n\,L(x_1,\ldots,x_n,\theta)\;.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5703}%
$ L(x_1,\ldots,x_n,\theta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5705}%
$ \widehat{\theta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5709}%
$\displaystyle \widehat{\theta} = \tau(x_1,\ldots,x_n) = \arg\max L(x_1,\ldots,x_n,\theta)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5715}%
$\displaystyle T = \tau(X_1,\ldots,X_n)\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5721}%
$\displaystyle f_\theta(x) = \frac{1}{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5722}%
$\displaystyle _{[0,\theta]}(x)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5726}%
$ x_1,\ldots,x_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5730}%
\begin{displaymath}\begin{array}{ccc}
L(x_1,\ldots,x_n,\theta) &=& 
\prod_{i=1}^n \frac{1}{\theta} \mbox{\rm\Large 1\hskip -0.353em 1}_{[0,\theta]}(x_i)\\ 
&=& \frac{1}{\theta^n} \mbox{\rm\Large 1\hskip -0.353em 1}_{[0,\theta]^n}(x_1,\ldots,x_n)\\ 
&=& \frac{1}{\theta^n}\mbox{\rm\Large 1\hskip -0.353em 1}_{[\max\{x_i\},+\infty[}(\theta)\;.
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5736}%
$ 1/\theta^n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5738}%
$\displaystyle \widehat{\theta} = \max\{x_1,\ldots,x_n\}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5746}%
$\displaystyle T=\max\{X_1,\ldots,X_n\}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5753}%
$ \log(L(x_1,\ldots,x_n,\theta))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5759}%
$ \{0,1\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5763}%
$ (x_1,\ldots,x_n)\in \{0,1\}^n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5765}%
$\displaystyle L(x_1,\ldots,x_n,p) = p^{\sum x_i}(1-p)^{n-\sum x_i}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5767}%
$\displaystyle \log(L(x_1,\ldots,x_n,p)) = (\sum x_i)\log p + (n-\sum x_i)\log(1-p)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5771}%
$\displaystyle \frac{\partial \log(L(x_1,\ldots,x_n,p))}{\partial p} = 
(\sum x_i)\frac{1}{p} - (n-\sum x_i)\frac{1}{1-p}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5773}%
$\displaystyle \widehat{p} = \frac{\sum x_i}{n}\;. 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5775}%
$\displaystyle \frac{\partial^2 \log(L(x_1,\ldots,x_n,p))}{\partial p^2} = 
-(\sum x_i)\frac{1}{p^2} - (n-\sum x_i)\frac{1}{(1-p)^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5777}%
$ \widehat{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5785}%
$\displaystyle \frac{\sum X_i}{n}\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5787}%
$ \mathbb{N}^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5789}%
$ p\in]0,1[$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5793}%
$\displaystyle L(x_1,\ldots,x_n,p) = p^{n}(1-p)^{\sum x_i-n}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5795}%
$\displaystyle \log(L(x_1,\ldots,x_n,p)) = n\log p + (\sum x_i-n)\log(1-p)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5799}%
$\displaystyle \frac{\partial \log(L(x_1,\ldots,x_n,p))}{\partial p} = 
n\frac{1}{p} - (\sum x_i-n)\frac{1}{1-p}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5801}%
$\displaystyle \widehat{p} = \frac{n}{\sum x_i}\;. 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5803}%
$\displaystyle \frac{\partial^2 \log(L(x_1,\ldots,x_n,p))}{\partial p^2} = 
-n\frac{1}{p^2} - (\sum x_i-n)\frac{1}{(1-p)^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5813}%
$\displaystyle \frac{n}{\sum X_i}\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5823}%
$\displaystyle L(x_1,\ldots,x_n,\lambda) = \prod_{i=1}^n \lambda e^{-\lambda x_i}
=\lambda^n e^{-\lambda \sum x_i}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5825}%
$\displaystyle \log(L(x_1,\ldots,x_n,\lambda)) = 
n\log(\lambda) - \lambda\sum x_i\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5829}%
$\displaystyle \frac{\partial \log(L(x_1,\ldots,x_n,\lambda))}{\partial \lambda} = 
n\frac{1}{\lambda} - \sum x_i\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5831}%
$\displaystyle \widehat{\lambda} = \frac{n}{\sum x_i}\;. 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5833}%
$\displaystyle \frac{\partial^2 \log(L(x_1,\ldots,x_n,\lambda))}{\partial \lambda^2} = 
- \frac{n}{\lambda^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5835}%
$ \widehat{\lambda}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5847}%
$ v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5855}%
$\displaystyle L(x_1,\ldots,x_n,\mu,v) = \prod_{i=1}^n \frac{1}{\sqrt{2\pi v}}
e^{-\frac{(x_i-\mu)^2}{2 v}}
=\left(\frac{1}{\sqrt{2\pi v}}\right)^n e^{-\frac{1}{2 v}\sum (x_i-\mu)^2}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5857}%
$\displaystyle \log(L(x_1,\ldots,x_n,\lambda)) = 
-\frac{n}{2}\log(v) - -\frac{n}{2}\log(2\pi) +\frac{1}{2 v}\sum (x_i-\mu)^2\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5863}%
$\displaystyle \frac{\partial \log(L(x_1,\ldots,x_n,\lambda))}{\partial \mu} = 
\frac{1}{v}\sum (x_i-\mu)\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5865}%
$\displaystyle \frac{\partial \log(L(x_1,\ldots,x_n,\lambda))}{\partial v} = 
-\frac{n}{2 v}+\frac{1}{2 v^2}\sum (x_i-\mu)^2\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5867}%
$\displaystyle \widehat{\mu} = \frac{\sum x_i}{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5868}%
$\displaystyle \quad
\widehat{v} =  \frac{\sum (x_i-\widehat{\mu})^2}{n}\;. 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5870}%
$\displaystyle \frac{\partial^2 \log(L(x_1,\ldots,x_n,\lambda))}{\partial \mu^2} =
-\frac{n}{v}\;, 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5872}%
$\displaystyle \frac{\partial^2 \log(L(x_1,\ldots,x_n,\lambda))}{\partial \mu\partial v} =
-\frac{1}{v^2}\sum(x_i-\mu)\;, 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5874}%
$\displaystyle \frac{\partial^2 \log(L(x_1,\ldots,x_n,\lambda))}{\partial v^2} =
-\frac{n}{2v^2}-\frac{1}{v^3}\sum(x_i-\mu)^2\;. 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5876}%
$ (\widehat{\mu},\widehat{v})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5878}%
\begin{displaymath}
\left(
\begin{array}{cc}
-\frac{n}{\widehat{v}}&0\\ 
0&-\frac{n}{2 \widehat{v}^2}
\end{array}
\right)\;.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5904}%
$ nF$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5906}%
$ {\cal B}(n,p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5908}%
$\displaystyle Q_{{\cal B}(100,0.523)}(0.95) = 60$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5909}%
$\displaystyle \quad
Q_{{\cal B}(100,0.682)}(0.05) = 60\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5917}%
$\displaystyle 60\in [\,Q_{{\cal B}(100,p)}(0.05)\,,\,Q_{{\cal B}(100,p)}(0.05)\,]\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5919}%
$ {\cal B}(100,p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5930}%
$ [T_1,T_2]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5932}%
$ T_1\leq T_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5934}%
$\displaystyle \mathbb{P}[\, \theta\in[T_1\,,\, T_2]\,]= 1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5940}%
$ T_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5942}%
$ T_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5944}%
$ t_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5946}%
$ t_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5948}%
$ \theta\in [t_1,t_2]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5964}%
$\displaystyle [Q_T(\alpha/2)\,,\,Q_T(1-\alpha/2)]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5970}%
$ [\underline{q}(\theta)\,,\,\overline{q}(\theta)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5976}%
$\displaystyle \mathbb{P}[\,T\in[\underline{q}(\theta)\,,\, \overline{q}(\theta)]\,] = 1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5982}%
$ \underline{q}(\theta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5984}%
$ \overline{q}(\theta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5992}%
$ \underline{q}^{-1}(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5994}%
$ \overline{q}^{-1}(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5997}%
$ \underline{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5999}%
$ \overline{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6001}%
$ [\overline{q}^{-1}(T)\,,\,\underline{q}^{-1}(T)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6009}%
$\displaystyle \theta\leq \underline{q}^{-1}(T) \;\Longleftrightarrow\; 
T\geq \underline{q}(\theta)\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6011}%
$\displaystyle \theta\geq \overline{q}^{-1}(T) \;\Longleftrightarrow\; 
T\leq \overline{q}(\theta)\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6013}%
$\displaystyle \theta\in [ \overline{q}^{-1}(T)\,,\,\underline{q}^{-1}(T)] 
\;\Longleftrightarrow\; 
T\in [\underline{q}(\theta)\,,\,\overline{q}(\theta)]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6027}%
$ T=\max\{X_1,\ldots,X_n\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6031}%
$ [\theta\alpha^{1/n},\theta]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6033}%
$\displaystyle \underline{q}(\theta) = \theta \alpha^{1/n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6034}%
$\displaystyle \quad
\overline{q}(\theta)=\theta\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6036}%
$\displaystyle \overline{q}^{-1}(t) = t$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6037}%
$\displaystyle \quad
\underline{q}^{-1}(t)=t\alpha^{-1/n}\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6039}%
$ [T,T\alpha^{-1/n}]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6053}%
$ \alpha=0.05$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6055}%
$\displaystyle 1.23\,(0.05)^{-1/100} = 1.267405\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6071}%
$\displaystyle \mathbb{P}[\,T\in [\underline{q}(\theta)\,,\,\overline{q}(\theta)]\,]\geq 1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6073}%
$\displaystyle \mathbb{P}[\, \theta\in[T_1\,,\, T_2]\,] \geq 1-\alpha.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6086}%
$\displaystyle \overline{X} = \frac{1}{n}\sum_{i=1}^n X_i$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6087}%
$\displaystyle \quad
S^2 = \frac{1}{n}\sum_{i=1}^n X_i^2 -\overline{X}^2\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6098}%
$ \displaystyle{\sqrt{\frac{n}{\sigma^2}}\Big(\overline{X}-\mu\Big)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6102}%
$ \displaystyle{\sqrt{\frac{n\!-\!1}{S^2}}\Big(\overline{X}-\mu\Big)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6104}%
$ {\cal T}(n\!-\!1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6106}%
$ \displaystyle{\frac{nS^2}{\sigma^2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6108}%
$ {\cal X}^2(n\!-\!1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6116}%
$ z_\alpha = Q_{{\cal N}(0,1)}(1-\alpha/2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6122}%
$ [-z_\alpha , z_\alpha]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6124}%
$ z_\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6130}%
$\displaystyle \mathbb{P}\left[\,\sqrt{\frac{n}{\sigma^2}}\Big(\overline{X}-\mu\Big)
\in[-z_\alpha,z_\alpha]\,\right] =1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6132}%
\begin{displaymath}\begin{array}{ccc}
\sqrt{\frac{n}{\sigma^2}}\Big(\overline{X}-\mu\Big)
\in[-z_\alpha,z_\alpha]
&\Longleftrightarrow&\overline{X}-\mu\in
\left[\,-z_\alpha\sqrt{\frac{\sigma^2}{n}}\,,\,
z_\alpha\sqrt{\frac{\sigma^2}{n}}\,\right] \\ 
&\Longleftrightarrow&
\mu\in
\left[\,\overline{X}-z_\alpha\sqrt{\frac{\sigma^2}{n}}\,,\,
\overline{X}+z_\alpha\sqrt{\frac{\sigma^2}{n}}\,\right]\;. 
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6134}%
$\displaystyle \left[\,\overline{X}-z_\alpha\sqrt{\frac{\sigma^2}{n}}\,,\,
\overline{X}+z_\alpha\sqrt{\frac{\sigma^2}{n}}\,\right]\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6144}%
$ {\cal T}(n-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6148}%
$ [-t_\alpha,t_\alpha]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6150}%
$\displaystyle t_\alpha = Q_{{\cal T}(n-1)}(1-\alpha/2)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6154}%
$\displaystyle \left[\,\overline{X}-t_\alpha\sqrt{\frac{S^2}{n-1}}\,,\,
\overline{X}+t_\alpha\sqrt{\frac{S^2}{n-1}}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6162}%
$ u_\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6164}%
$ v_\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6166}%
$ [u_\alpha,v_\alpha]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6172}%
$\displaystyle u_\alpha =Q_{{\cal X}^2(n-1)}(\alpha/2)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6173}%
$\displaystyle \quad 
v_\alpha =Q_{{\cal X}^2(n-1)}(1-\alpha/2)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6175}%
$\displaystyle \mathbb{P}\left[\,\frac{nS^2}{\sigma^2} \in [u_\alpha\,,\,v_\alpha] \,\right] 
= 1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6177}%
$\displaystyle \frac{nS^2}{\sigma^2} \in [u_\alpha,v_\alpha]\;\Longleftrightarrow\;
\sigma^2\in \left[\,\frac{nS^2}{v_\alpha}\,,\,\frac{nS^2}{u_\alpha}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6179}%
$ \left[\,\frac{nS^2}{v_\alpha}\,,\,\frac{nS^2}{u_\alpha}\,\right]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6208}%
$\displaystyle Y_i = a x_i + b +E_i\;,
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6210}%
$ E_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6212}%
$ {\cal N}(0,\sigma^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6216}%
$ ax_i+b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6243}%
$ EQ(A,B)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6245}%
$ (n\!-\!2)\sigma^2/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6249}%
$\displaystyle V=\frac{n}{n-2} EQ(A,B)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6251}%
$ x_*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6255}%
$ Y_*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6257}%
$ {\cal N}(ax_*+b,\sigma^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6259}%
$ Ax_*+B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6264}%
$ \displaystyle{\sqrt{\frac{ns_x^2}{\sigma^2}}(A-a)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6268}%
$ \displaystyle{\sqrt{\frac{ns_x^2}{V}}(A-a)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6270}%
$ {\cal T}(n-2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6272}%
$ \displaystyle{\sqrt{\frac{ns_x^2}{\sigma^2(s_x^2+(x^*-\overline{x})^2)}}
(Ax^*+B-ax^*-b)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6276}%
$ \displaystyle{\sqrt{\frac{ns_x^2}{V(s_x^2+(x^*-\overline{x})^2)}}
(Ax^*+B-ax^*-b)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6280}%
$ \displaystyle{(n-2)\frac{V}{\sigma^2}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6282}%
$ {\cal X}^2(n\!-\!2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6296}%
$ {\cal X}^2(n-2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6304}%
$\displaystyle \left[\,A-z_\alpha\sqrt{\frac{\sigma^2}{ns_x^2}}\;,\;
A+z_\alpha\sqrt{\frac{\sigma^2}{ns_x^2}}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6310}%
$\displaystyle \left[\,A-t_\alpha\sqrt{\frac{V}{ns_x^2}}\;,\;
A+t_\alpha\sqrt{\frac{V}{ns_x^2}}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6312}%
$ ax_*+b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6316}%
$\displaystyle \left[\,Ax_*+B-z_\alpha
\sqrt{\frac{\sigma^2(s_x^2+(x^*-\overline{x})^2)}{ns_x^2}}\;,\;
Ax_*+B+z_\alpha\sqrt{\frac{\sigma^2(s_x^2+(x^*-\overline{x})^2)}{ns_x^2}}
\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6322}%
$\displaystyle \left[\,Ax_*+B-t_\alpha
\sqrt{\frac{V(s_x^2+(x^*-\overline{x})^2)}{ns_x^2}}\;,\;
Ax_*+B+t_\alpha\sqrt{\frac{V(s_x^2+(x^*-\overline{x})^2)}{ns_x^2}}
\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6326}%
$\displaystyle \left[\,(n-2)\frac{V}{v_\alpha}\;,\;(n-2)\frac{V}{u_\alpha}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6328}%
$ Y_*=ax_*+b+E_*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6334}%
$ E_*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6344}%
$\displaystyle \left[\,Ax_*\!+\!B-t_\alpha
\sqrt{\frac{V((n\!+\!1)s_x^2+(x^*\!-\!\overline{x})^2)}{ns_x^2}}\;,\;
Ax_*\!+\!B+t_\alpha
\sqrt{\frac{V((n\!+\!1)s_x^2+(x^*\!-\!\overline{x})^2)}{ns_x^2}}
\,\right]\,.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6348}%
$ y_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6383}%
\begin{displaymath}
\begin{array}{|cccccccc|}
\hline
\overline{x}&\overline{Y}&s_x^2&s_Y^2&r_{xY}&A&B&
EQ(A,B)\\ 
\hline
113.2&20.3&34.76&7.61&0.9&0.42&-27.38&1.44\\ 
\hline
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6397}%
$ \overline{x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6407}%
$ T_{1,n}\leq T_{2,n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6411}%
$ [T_{1,n}\,,\,T_{2,n}]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6417}%
$\displaystyle \lim_{n\rightarrow\infty}\mathbb{P}[ \theta \in [T_{1,n}\,,\,T_{2,n}]\,]=1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6432}%
$\displaystyle Z_n = \sqrt{\frac{n}{\sigma^2}}(\overline{X}_n-\mu)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6433}%
$\displaystyle \quad
Z'_n = \sqrt{\frac{n}{S^2_n}}(\overline{X}_n-\mu)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6435}%
$ Z_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6437}%
$ Z'_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6447}%
$ [-z_\alpha\,,\,z_\alpha]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6451}%
$\displaystyle \lim_{n\rightarrow\infty} \mathbb{P}[\, Z_n\in [-z_\alpha\,,\,z_\alpha]\, ]
=
\lim_{n\rightarrow\infty} \mathbb{P}[\, Z'_n\in [-z_\alpha\,,\,z_\alpha]\, ]
=1-\alpha\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6457}%
$\displaystyle \left[\,\overline{X}_n-z_\alpha\sqrt{\frac{\sigma^2}{n}}\,,\,
\overline{X}_n+z_\alpha\sqrt{\frac{\sigma^2}{n}}\,\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6458}%
$\displaystyle \quad
\left[\,\overline{X}_n-z_\alpha\sqrt{\frac{S^2_n}{n}}\,,\,
\overline{X}_n+z_\alpha\sqrt{\frac{S^2_n}{n}}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6468}%
$ u\in]0,1[$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6470}%
$ Q(u)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6472}%
$ u=0.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6478}%
$ u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6482}%
$ X_{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6486}%
$ i\!-\!1<nu\leq i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6496}%
$\displaystyle f_{T_n}(x) = \frac{n!}{(i-1)!(n-i)!}F^{i-1}(x)(1-F(x))^{n-i}f(x)\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6505}%
$\displaystyle Z_n = f(Q(u))\sqrt{\frac{n}{u(1-u)}}(T_n-Q(u))\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6515}%
$\displaystyle \left[\,T_n - z_\alpha \frac{\sqrt{u(1-u)}}{f(Q(u))\sqrt{n}}\,,\,
T_n + z_\alpha \frac{\sqrt{u(1-u)}}{f(Q(u))\sqrt{n}}\,\right]\;.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6523}%
$ {\cal P}(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6525}%
$ {\cal G}(n,\lambda)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6529}%
$ {\cal B}(10,0.5)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6531}%
$ {\cal B}(10,0.2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6533}%
$ {\cal B}(100,0.2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6535}%
$ {\cal P}(30)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6537}%
$ {\cal P}(100)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6539}%
$ {\cal P}(200)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6541}%
$ D_{KS}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6543}%
$ {\cal G}(10,1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6545}%
$ {\cal G}(50,1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6547}%
$ {\cal G}(100,1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6549}%
$ {\cal X}^2(30)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6551}%
$ {\cal X}^2(50)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6553}%
$ {\cal X}^2(100)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
