3.1.1随机事件的概率的Breamer(2018-03-22)

% !Mode:: "TeX:UTF-8"
\documentclass[xcolor=svgnames,serif,table,12pt]{beamer}%,
%\includeonlyframes{Representation}%Acknowledgement
\mode<presentation>{
% Setup appearance:
\setbeamercovered{transparent}
\usecolortheme[named=FireBrick]{structure}
\setbeamertemplate{caption}[numbered]
\setbeamertemplate{navigation symbols}{}

\useoutertheme{infolines}
\usetheme{Darmstadt}

\setbeamertemplate{blocks}[rounded][shadow=true]
\setbeamercovered{transparent}
\usepackage{hyperref}
% 修改样式
%\setbeamertemplate{blocks}[rounded][shadow=true]

\setbeamercolor{box}{bg=black!20!orange,fg=white}

\setbeamercolor{block title}{use=sidebar,fg=sidebar.fg!10!white,bg=orange!70!black}
%\setbeamercolor{block body}{use=sidebar,fg=black,bg=sidebar.bg!90!blue}

\setbeamercolor{block title example}{use=sidebar,fg=sidebar.fg!10!white,bg=black!60!green}
%\setbeamercolor{block body example}{use=sidebar,fg=black,bg=sidebar.bg!90!green}

\setbeamercolor{block title alerted}{use=sidebar,fg=sidebar.fg!10!white,bg=black!50!red}
%\setbeamercolor{block body alerted}{use=sidebar,fg=black,bg=sidebar.bg!90!red}

\setbeamerfont{frametitle}{size=\small,series=\CJKfamily{FZDH}\Arial\boldmath}
%\setbeamerfont{frametitle}{series=\bfseries}

\setbeamertemplate{headline}
{%
  \begin{beamercolorbox}[shadow=true]{section in head/foot}
  \vskip2pt\insertnavigation{\paperwidth}\vskip2pt
  \end{beamercolorbox}%
}

\iffalse
\AtBeginSection[]
{
  \frame{
    \footnotesize
    \frametitle{主要内容}
    \tableofcontents[currentsection]
  }
}

\AtBeginSubsection[]
{
  \begin{frame}
    \footnotesize
    \frametitle{主要内容}
    \tableofcontents[currentsection,currentsubsection]
  \end{frame}
}
\fi

\renewcommand{\raggedright}{\leftskip=0pt \rightskip=0pt plus 0cm}
\raggedright
}

\usepackage{tabularx,multirow,multicol,longtable}
\usepackage{tabu}
\usepackage{graphics}
\usepackage{xcolor}
\usepackage[no-math]{fontspec}%--------------------------------------------------提供字体选择命令
\usepackage{xunicode}%-----------------------------------------------------------提供Unicode字符宏
\usepackage{xltxtra}%------------------------------------------------------------提供了针对XeTeX的改进并且加入了XeTeX的LOGO
\usepackage[BoldFont,SlantFont,CJKchecksingle]{xeCJK}%---------------------------使用xeCJK宏包
%================================== 设置中文字体 ================================%
\setCJKmainfont{Adobe Heiti Std}%------------------------------------------------设置正文为黑体
\setCJKmonofont{Adobe Song Std}%-------------------------------------------------设置等距字体
\setCJKsansfont{Adobe Kaiti Std}%------------------------------------------------设置无衬线字体
\setCJKfamilyfont{zxzt}{FZShouJinShu-S10S}
\setCJKfamilyfont{FZDH}{FZDaHei-B02S}
%================================== 设置中文字体 ================================%

%================================== 设置英文字体 ================================%
\setmainfont[Mapping=tex-text]{TeX Gyre Pagella}%--------------------------------英文衬线字体
\setsansfont[Mapping=tex-text]{Trebuchet MS}%------------------------------------英文无衬线字体
\setmonofont[Mapping=tex-text]{Courier New}%-------------------------------------英文等宽字体
\newfontfamily\Arial{Arial}
%================================== 设置英文字体 ================================%

%================================== 设置数学字体 ================================%
%\setmathsfont(Digits,Latin,Greek)[Numbers={Lining,Proportional}]{Minion Pro}
%================================== 设置数学字体 ================================%
\punctstyle{kaiming}%------------------------------------------------------------开明式标点格式
\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{positioning,backgrounds}
\usetikzlibrary{fadings}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}
\usetikzlibrary{shadings}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}
\usepackage{xifthen}
\usepackage{colortbl,dcolumn}
\usepackage{enumerate}
\usepackage{pifont}
\usepackage{tabularx}
\usepackage{booktabs}

%=================================== 数学符号 =================================%
\newcommand{\rtn}{\mathrm{\mathbf{R}}}
\newcommand{\N}{\mathrm{\mathbf{N}}}
\newcommand{\As}{\mathrm{a.s.}}
\newcommand{\Ae}{\mathrm{a.e.}}
\newcommand*{\PR}{\mathrm{\mathbf{P}}}
\newcommand*{\EX}{\mathrm{\mathbf{E}}}
\newcommand{\EXlr}[1]{\mathrm{\mathbf{E}}\left[#1\right]}
\newcommand*{\dif}{\,\mathrm{d}}
\newcommand*{\F}{\mathcal{F}}
\newcommand*{\h}{\mathcal{H}}
\newcommand*{\vp}{\varepsilon}
\newcommand*{\prs}{\dif\PR-\As}
\newcommand*{\dte}{\dif t-\Ae}
\newcommand*{\pts}{\dif\PR\times\dif t-\Ae}
\newcommand{\Ito}{It\^{o}}
\newcommand{\tT}[1][0]{[#1,T]}
\newcommand{\intT}[2][T]{\int^{#1}_{#2}}
\newcommand{\intTe}[1][t]{\intT[t+\varepsilon]{#1}}
\newcommand{\s}{\mathcal{S}}
\newcommand{\me}{\mathrm{e}}
\newcommand{\one}[1]{{\bf 1}_{#1}}
\renewcommand{\M}{{\rm M}}
\newcommand{\Me}[1][t]{M^{\varepsilon}_{#1}}
\newcommand{\Ne}[1][t]{N^{\varepsilon}_{#1}}
\newcommand{\Pe}[1][t]{P^{\varepsilon}_{#1}}
\DeclareMathOperator*{\sgn}{sgn}
%=================================== 数学符号 =================================%

\graphicspath{{figures/}}

\title[随机事件的概率]{\Huge\bfseries 3.1.1 随机事件的概率}

\author[wsx]{wsx}

\institute[lpssz]{\includegraphics[width=2cm]{lpssz}\\ lpssz}

\date{2018-03-22}

\setlength{\baselineskip}{22pt}
\renewcommand{\baselinestretch}{1.4}

\begin{document}

\setlength{\abovedisplayskip}{1ex}%------------------------------------------ 公式前的距离
\setlength{\belowdisplayskip}{1ex}%------------------------------------------ 公式后的距离

%\includeonlyframes{Brown}

\begin{frame}
  \titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}{\Huge 第三章\quad 概率}
\begin{figure}
\vskip-6.5em% \hskip-6em
\includegraphics[page=1,scale=0.60]{mindmap}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 概率论的由来}
相传，两位著名的数学家Pascal和Fermat经常在巴黎的咖啡屋里碰面讨论深奥的数学问题，为了解乏，他们经常玩一个简单的游戏.
\begin{figure}
\includegraphics[scale=0.4]{paris}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 概率论的由来}
重复抛掷硬币---每次正面朝上Pascal得一分，反面朝上Fermat得一分.一方先得三分，另一方就买单.\\\pause
一天，他们抛掷一次硬币，出现正面朝上（Pascal得一分）, Fermat有急事必须离开. 之后他们就想应该由谁来买单呢？ 
 或者采用分摊，怎么分摊才合理呢？
\end{frame}
\begin{frame}{\Huge 3.1.1 随机事件的概率}
\begin{figure}
\vskip-6.5em% \hskip-6em
\includegraphics[page=2,scale=0.60]{mindmap}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 情景引入}
有四张红色卡片，分别编号为1,2,3,4，从中抽取一张卡片
 \begin{itemize}
\item “抽到的卡片是红色的”
 \item “抽到的卡片是蓝色的” 
\item “抽到的卡片编号是1号”
  \end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 事件的分类}
 \begin{itemize}\pause
\item \alert{必然事件}：在条件S下，一定会发生的事件.\pause
    \item \alert{不可能事件}：在条件S下，一定不会发生的事件.\pause
    \item \alert{随机事件}：在条件S下，可能发生也可能不发生的事件.\pause
\item {\centering 必然事件和不可能事件称为\alert{确定事件}.}\pause
\item 确定事件和随机事件统称为\alert{事件},一般用大写字母$A,B,C$…表示.\pause
  \end{itemize}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 事件的分类 }
 判断下列事件哪些是必然事件，哪些是不可能事件，哪些是随机事件？\\
%\begin{enumerate}
(1)“抛一块石头，下落”；\\
(2)“某人射击一次,中靶”;\\
(3)“从分别标有1,2,3,4,5的5张标签中任取1张,得到4号签”;\\
(4)“掷一枚硬币,出现正面”;\\
(5)“没有水分,种子能发芽”;\\
(6)“在常温下,焊锡熔化”
%\end{enumerate}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 随机事件的概率}
对于随机事件，我们知道它发生的可能性的大小事非常重要的。那么我们用什么来度量随机事件发生的可能性的大小呢？\\ \pause
\begin{block}{}
用\alert{概率}度量随机事件发生的可能性大小.
  \end{block}\pause
如何获得随机事件发生的概率？
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 试验}
第一步，全班同学各取一枚相同的硬币，做$10$次抛硬币试验，每人记录下试验结果，填在下表中：\\
\begin{center}
  \setlength{\extrarowheight}{1.5mm}
  %\addtolength{\tabcolsep}{1mm}
  \rowcolors[]{1}{orange!70}{white!90!gray}
   \begin{tabular}{|c|c|c|c|}
     姓名         & 试验次数&正面朝上的次数&正面朝上的比例 \\\hline
           & &  & \\\hline
    \end{tabular}
 \end{center}
{\Huge \bfseries 思考 } \quad 与其他同学的试验结果比较，你的结果和他们一致吗？为什么会出现这样的情况？

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 试验}
第二步，每个小组把本组同学的试验结果统计一下，填入下表：\\
\begin{center}
  \setlength{\extrarowheight}{1.5mm}
  %\addtolength{\tabcolsep}{1mm}
  \rowcolors[]{1}{orange!70}{white!90!gray}
   \begin{tabular}{|c|c|c|c|}
     组次        & 试验总次数&正面朝上的总次数&正面朝上的比例 \\\hline
           & &  & \\\hline
    \end{tabular}
 \end{center}
{\Huge \bfseries 思考 } \quad 与其他小组的试验结果比较，各种的结果一致吗？为什么？
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 试验}
第三步，请一个同学把全班同学的试验结果统计一下，填入下表：\\
\begin{center}
  \setlength{\extrarowheight}{1.5mm}
  %\addtolength{\tabcolsep}{1mm}
  \rowcolors[]{1}{orange!70}{white!90!gray}
   \begin{tabular}{|c|c|c|c|}
     班级        & 试验总次数&正面朝上的总次数&正面朝上的比例 \\\hline
           & &  & \\\hline
    \end{tabular}
 \end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 试验}
第四步，请把全班每个同学的试验中正面朝上的次数收集起来，并用条形图表示.\\
\vskip6.5em
{\Huge \bfseries 观察 } \quad 这个条形图有什么特点？

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 试验}
第五步，请同学们找出抛硬币时“正面朝上”这个事件发生的规律性.\\
\vskip6.5em
{\Huge \bfseries 探究 } \quad 如果同学们再重复一次上面的试验，全班的汇总结果还会和这次的汇总结果一致吗？如果不一致，你能说出原因吗？
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 基本概念}
\begin{block}{频数}
在相同的条件$S$下重复$n$次试验，观察某一个事件$A$是否出现，称$n$次试验中事件A出现的次数$n_A$为事件$A$出现的频数.
  \end{block}\pause
\begin{block}{频率}
我们称事件$A$出现的比例$f_n(A)=\dfrac{n_A}{n}$为事件出现的频率.
  \end{block}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 计算机模拟掷硬币试验}
\begin{figure}
\includegraphics[scale=0.25]{computer}
\end{figure}\pause
\begin{block}{}
在大量重复试验后,随着试验次数的增加，“正面朝上”的频率
\alert{逐渐稳定}在0.5的附近.
  \end{block}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 历史上一些掷硬币的试验结果}
\begin{center}
  \setlength{\extrarowheight}{1.5mm}
  %\addtolength{\tabcolsep}{1mm}
  \rowcolors[]{1}{orange!70}{white!90!gray}
   \begin{tabular}{|c|c|c|}
      试验次数&正面朝上的次数&正面朝上的比例 \\\hline
       2048    &1061 & 0.5181 \\
4040&2048&0.5069\\
12000&6019&0.5016\\
24000&12012&0.5005\\
30000&14984&0.4995\\
72088&36124&0.5011\\\hline
    \end{tabular}
 \end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 规律总结 }
由以上试验的规律，得到在一般情况下随机事件A的规律：\\
 \begin{block}{}
一般来说,在大量重复进行同一试验时,随着试验次数的增加,事件A发生的频率$f_n(A)=\dfrac{n_A}{n}$会逐渐稳定在区间$[0,1]$中的某个\alert{常数}上.\pause 这个常数叫做事件A的\alert{概率}，记作$P(A)$.\\
  \end{block}
  \begin{block}{大数定律}
1713年，瑞士数学家雅各布·贝努利(Jacob Bernouli)对这一客观规律性从理论上给予了证明，并提出了著名的大数定律：\alert{随着试验次数的增加，频率稳定在概率附近.}.
  \end{block}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 例题 }
例1 某运动员在同一条件下进行射击,结果如下表所示:
\begin{center}
  \setlength{\extrarowheight}{1.5mm}
  %\addtolength{\tabcolsep}{1mm}
  \rowcolors[]{1}{orange!70}{white!90!gray}
   \begin{tabular}{|c|c|c|c|c|c|c|}
射击次数$n$    &10    &20&    50&    100&    200&    500\\\hline
击中靶心次数$n_A$&    8&    19&    44&    92&    178&    455\\\hline
击中靶心的频率&&&&&&    \\\hline
    \end{tabular}
 \end{center}

                    
 \begin{block}{}
(1)填写表中击中靶心的频率;
  \end{block}
  \begin{block}{}
(2)这个运动员射击一次,击中靶心的概率约是多少?
  \end{block}
\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 小组讨论}
%\Lauge

 \begin{itemize}
    \item 事件$A$发生的\alert{频率}是不是不变的？
    \item 事件$A$发生的\alert{概率}是不是不变的？
\item 它们之间有什么\alert{区别与联系}？
  \end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 区别与联系}\pause

  \begin{block}{区别：}
频率本身是随机的,在试验前不能确定,做同样次数或不同次数的重复试验得到的事件的频率都可能不同.而概率是一个确定数,是客观存在的,与每次试验无关.
  \end{block}\pause

  \begin{block}{联系：}
随着试验次数的增加, 频率会在概率的附近摆动,并趋于稳定.在实际问题中,若事件的概率未知,常用频率作为它的估计值.
  \end{block}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{\Huge 作业}
\Huge 课本P113练习1，2
\end{frame}


\begin{frame}{}
  \begin{center}
    \begin{tikzpicture}
      \node[above,xscale=1.2,yscale=1.4]{\Huge\bfseries 谢谢!};
      \node[xscale=1.2,above,yscale=-1.4,scope fading=south,opacity=0.2]{\Huge\bfseries 谢谢!};
    \end{tikzpicture}
  \end{center}
\end{frame}

\end{document}