From ceffff7c56cdad571f729767b4225a7011170233 Mon Sep 17 00:00:00 2001 From: Didnelpsun <2675350965@qq.com> Date: Wed, 14 Jul 2021 23:14:08 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E9=9A=8F=E6=9C=BA=E5=8F=98?= =?UTF-8?q?=E9=87=8F=E6=95=B0=E5=AD=97=E7=89=B9=E5=BE=81?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../random-variables-and-distribution.pdf | Bin 66872 -> 76386 bytes .../random-variables-and-distribution.tex | 57 +++++ .../random-variables-and-distribution.pdf | Bin 145283 -> 179723 bytes .../random-variables-and-distribution.tex | 228 +++++++++++++++++- .../3-digital-features/digital-features.pdf | Bin 0 -> 48810 bytes .../3-digital-features/digital-features.tex | 39 ++- 6 files changed, 320 insertions(+), 4 deletions(-) create mode 100644 probability-theory-and-mathematical-statistics/knowledge/3-digital-features/digital-features.pdf diff --git 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a/probability-theory-and-mathematical-statistics/exercise/2-random-variables-and-distribution/random-variables-and-distribution.tex +++ b/probability-theory-and-mathematical-statistics/exercise/2-random-variables-and-distribution/random-variables-and-distribution.tex @@ -22,6 +22,10 @@ % 数学公式 \usepackage[colorlinks,linkcolor=black,urlcolor=blue]{hyperref} % 超链接 +\usepackage{tikz} +% 绘图 +\usepackage{multicol} +% 分栏 \author{Didnelpsun} \title{随机变量及其分布} \date{} @@ -88,6 +92,59 @@ $\therefore P\{a1\}$。 + +解:求$P\{X+Y>1\}$就是求一个区间的概率值,即$P\{(X,Y)\in G\}=\iint\limits_Gf(x,y)\,\textrm{d}x\textrm{d}y$。 + +\begin{multicols}{2} + + \begin{tikzpicture}[scale=2] + \draw[-latex](-0.25,0) -- (1.25,0) node[below]{$x$}; + \draw[-latex](0,-0.25) -- (0,1.25) node[above]{$y$}; + \filldraw[black] (0,0) node[below]{$O$}; + \draw[black](1,0) -- (0,1) node[left]{$1$}; + \draw[black](1,1) -- (1,0) node[below]{$1$}; + \draw[black](0,0) -- (1,1); + \draw[black, densely dashed](0.5,0.5) -- (0.5,0) node[below]{$\dfrac{1}{2}$}; + \filldraw [fill=gray!50] (0.5,0.5) -- (1,1) -- (1,0) -- (0.5,0.5); + \draw[black](0.8,0.5) node{$D$}; + \draw[black, densely dashed](0.6,0) -- (0.6,1) node[above]{$y=y_0$}; + \end{tikzpicture} + + 所以$P\{X+Y>1\}=\iint\limits_D\dfrac{1}{x}\textrm{d}\delta$,$D=x+y>1\cap0a\}$。 diff --git a/probability-theory-and-mathematical-statistics/knowledge/2-random-variables-and-distribution/random-variables-and-distribution.pdf b/probability-theory-and-mathematical-statistics/knowledge/2-random-variables-and-distribution/random-variables-and-distribution.pdf index c4408848b2b543de8b4aa0d8c5200922b637567b..77ea3e221cf2c275bb965e2ce558d55e3906dfe1 100644 GIT binary patch delta 164018 zcmZU)Q;aSQ5F|RbZQHhO+qTW~jcpreY|k0nwr$(oe>XRq-Mep{bkYy?(CMnK3ciJk z{(`AL0tMzuL?#0;GqJG?2*9|yxtJTHX-3qS`%P^(SKW0dOGHx}3DH#G_ zb;ROtC2A@2u$RVPQF;yKyCyR!&21FBly4#(<+`S`4dwip_Tz;P!Z4>Ple|bN^--^< z^C6_JY9j#>#^$##E?izb5JUWVWPfKPPrvf(-o3_viq~zSUU1OB+B1SCK9-w6Ag~Qg 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