matlab連續(xù)型隨機(jī)變量的分布.doc

連續(xù)型隨機(jī)變量的分布及其數(shù)字特征一、基本概念設(shè)隨機(jī)變量X的分布函數(shù)為F(x)，若存在非負(fù)函數(shù)f(x)，使對(duì)任意實(shí)數(shù)x，有≤X{P????xd}則稱X為連續(xù)型隨機(jī)變量，并稱f(x)為X的概率密度，它滿足以下性質(zhì)：①f(x)≥0，-∞＜x＜+∞;②;③P{a0，則稱X服從參數(shù)為和2的正態(tài)分布，記作X～N(???,2)．當(dāng)=0，=1時(shí)，稱X服從標(biāo)準(zhǔn)正態(tài)分布，記作X～N(0,1)．MATLAB提供的有關(guān)正態(tài)分布的函數(shù)如下：normpdf(X,M,C)正態(tài)分布的密度函數(shù)normcdf(X,M,C)正態(tài)分布的累積分布函數(shù)norminv(P,M,C)正態(tài)分布的逆累積分布函數(shù)normrnd(M,C,m,n)產(chǎn)生服從正態(tài)分布的隨機(jī)數(shù)normstat(M,C)求正態(tài)分布的數(shù)學(xué)期望和方差其中X為隨機(jī)變量，M為正態(tài)分布參數(shù)，C為參數(shù)，P為顯著概率，m和n為隨機(jī)矩陣??的行數(shù)和列數(shù)．繪制標(biāo)準(zhǔn)正態(tài)分布的密度函數(shù)及累積分布函數(shù)圖和一般正態(tài)分布的密度函數(shù)及累積分布函數(shù)圖的程序如下：x=-4:0.01:4;y=normpdf(x,0,1);z=normcdf(x,0,1);-0.100.10.20.305101520-0.100.10.20.300.51-4-202400.20.4-4-202400.5105101500.20.40.605101500.51subplot(2,2,1);plot(x,y, k );axis([-4,4,-0.1,0.5]);subplot(2,2,2);plot(x,z, k );axis([-4,4,-0.1,1.1]);x=-4:0.01:16;y1=normpdf(x,6,1);z1=normcdf(x,6,1);y2=normpdf(x,6,4);z2=normcdf(x,6,4);y3=normpdf(x,6,0.6);z3=normcdf(x,6,0.6);subplot(2,2,3);plot(x,y1, k ,x,y2, k ,x,y3, k );axis([-4,16,-0.1,0.8]);subplot(2,2,4);plot(x,z1, k ,x,z2, k ,x,z3, k );axis([-4,16,-0.1,1.1]);三、求解方法(1)通用函數(shù)介紹.Pdf計(jì)算已選函數(shù)的概率密度函數(shù),調(diào)用格式為:Y=Pdf(name,X,A)Y=Pdf(name,X,A,B)Y=Pdf(name,X,A,B,C)Name為上表中取stat后的字符，如beta、bino、chiz、exp等。(2)利用專用函數(shù).Betapdf(X1，A1，B)Binopaf(X,N,P)四、例題繪制卡方分布密度函數(shù)在n分別等于1，5，15時(shí)的值>>x=0:0.2:30y1=chi2pdf(x,1)plot(x,y1, + )holdony2=chi2pdf(x,5)plot(x,y2, + )y2=chi2pdf(x,15)plot(x,y2, o )axis([0,30,0,0.2])Columns1through1300.20000.40000.60000.80001.00001.20001.40001.60001.80002.00002.20002.4000Columns14through262.60002.80003.00003.20003.40003.60003.80004.00004.20004.40004.60004.80005.0000Columns27through395.20005.40005.60005.80006.00006.20006.40006.60006.80007.00007.20007.40007.6000Columns40through527.80008.00008.20008.40008.60008.80009.00009.20009.40009.60009.800010.000010.2000Columns53through6510.400010.600010.800011.000011.200011.400011.600011.800012.000012.200012.400012.600012.8000Columns66through7813.000013.200013.400013.600013.800014.000014.200014.400014.600014.800015.000015.200015.4000Columns79through9115.600015.800016.000016.200016.400016.600016.800017.000017.200017.400017.600017.800018.0000Columns92through10418.200018.400018.600018.800019.000019.200019.400019.600019.800020.000020.200020.400020.6000Columns105through11720.800021.000021.200021.400021.600021.800022.000022.200022.400022.600022.800023.000023.2000Columns118through13023.400023.600023.800024.000024.200024.400024.600024.800025.000025.200025.400025.600025.8000Columns131through14326.000026.200026.400026.600026.800027.000027.200027.400027.600027.800028.000028.200028.4000Columns144through15128.600028.800029.000029.200029.400029.600029.800030.0000y1=Columns1through13Inf0.80720.51640.38150.29900.24200.19990.16740.14170.12090.10380.08950.0776Columns14through260.06740.05880.05140.04500.03950.03480.03060.02700.02380.02110.01860.01650.0146Columns27through390.01300.01150.01030.00910.00810.00720.00640.00570.00510.00460.00410.00360.0032Columns40through520.00290.00260.00230.00210.00180.00170.00150.00130.00120.00110.00090.00090.0008Columns53through650.00070.00060.00050.00050.00040.00040.00040.00030.00030.00030.00020.00020.0002Columns66thro

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