From df3ea3228eed431de40e70d236ed3116d3ad43f4 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Fri, 12 Aug 2022 23:09:30 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- linear-algebra/exercise/5-similar/similar.pdf | Bin 85475 -> 85219 bytes linear-algebra/exercise/5-similar/similar.tex | 15 +- .../6-quadratic-form/quadratic-form.pdf | Bin 12936 -> 66904 bytes .../6-quadratic-form/quadratic-form.tex | 187 ++++++++++++++++++ .../6-quadratic-form/quadratic-form.pdf | Bin 162488 -> 92968 bytes .../6-quadratic-form/quadratic-form.tex | 176 ----------------- .../random-events-and-probability.pdf | Bin 69551 -> 64956 bytes .../random-events-and-probability.tex | 14 +- 8 files changed, 206 insertions(+), 186 deletions(-) diff --git a/linear-algebra/exercise/5-similar/similar.pdf b/linear-algebra/exercise/5-similar/similar.pdf index 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O@*SR>Tueb6{(k_I%_718 diff --git a/probability-theory-and-mathematical-statistics/exercise/1-random-events-and-probability/random-events-and-probability.tex b/probability-theory-and-mathematical-statistics/exercise/1-random-events-and-probability/random-events-and-probability.tex index 9eac873..dad3567 100644 --- a/probability-theory-and-mathematical-statistics/exercise/1-random-events-and-probability/random-events-and-probability.tex +++ b/probability-theory-and-mathematical-statistics/exercise/1-random-events-and-probability/random-events-and-probability.tex @@ -87,15 +87,19 @@ $ABC$都不发生就是$A$不发生且$B$不发生且$C$不发生,用式子表 又事件$AB$相互独立。$P(\overline{AB})=P(\overline{A})P(\overline{B})=(1-a)(1-b)$。 -\section{概率模型} +\section{古典概型} -\subsection{古典概型} +\subsection{定义法} -\textbf{例题:}设袋中黑白球各一个,有放回取球,每次取一个,直到两种颜色的球都取到为止。求取球次数恰为3的概率。 +\subsection{随机分配} -解:若是看到题目中的为止,很容易想到后面的几何概率分布。但是这与几何分布不同,因为几何分布要求的停止条件是同一个事件的前几次的失败和最后一次的成功,而这个题目要求是取到黑并且取到白,而不是取到黑或取到白这两个事件,如求取到黑时取求次数为3的概率,则是几何分布。 +将$n$个质点分配倒$N$个容器中: -每次可能取到黑白两种,取三次,则事件总数为$2^3=8$。而取到第三次才取到黑白两色的,则有黑黑白、白白黑两种可能性,所以概率为$\dfrac{2}{8}=\dfrac{1}{4}$。 +% \textbf{例题:}设袋中黑白球各一个,有放回取球,每次取一个,直到两种颜色的球都取到为止。求取球次数恰为3的概率。 + +% 解:若是看到题目中的为止,很容易想到后面的几何概率分布。但是这与几何分布不同,因为几何分布要求的停止条件是同一个事件的前几次的失败和最后一次的成功,而这个题目要求是取到黑并且取到白,而不是取到黑或取到白这两个事件,如求取到黑时取求次数为3的概率,则是几何分布。 + +% 每次可能取到黑白两种,取三次,则事件总数为$2^3=8$。而取到第三次才取到黑白两色的,则有黑黑白、白白黑两种可能性,所以概率为$\dfrac{2}{8}=\dfrac{1}{4}$。 \section{独立性}