设随机变量X服从二项分布b(2,p),随机变量Y服从二项分布b(3,p)，若P(X≥1)=5/9,则P(Y≥1)=? 设随机变量X服从二项分布B(2, p)，已知P{X≥1}=5...
\u8bbe\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u4e8c\u9879\u5206\u5e03b(2,p),\u968f\u673a\u53d8\u91cfY\u670d\u4ece\u4e8c\u9879\u5206\u5e03b(4,p)\uff0c\u82e5P(X\u22651)=5/9,\u5219P(Y\u22651)=?\u8bbe\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u4e8c\u9879\u5206\u5e03b\uff082\uff0cp\uff09\uff0c\u968f\u673a\u53d8\u91cfY\u670d\u4ece\u4e8c\u9879\u5206\u5e03b\uff084\uff0cp\uff09\uff0c\u82e5P\uff08X\u22651\uff09\uff1d5\uff0f9\uff0c\u5219P\uff08Y\u22651\uff09\uff1d65\uff0f81\u3002
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\u4f60\u597d\uff0c
p(x=0)=1-p(x>=1)=1-5/9=4/9
\u6839\u636e\u4e8c\u9879\u5206\u5e03\u7684\u516c\u5f0f\uff0c\u53ef\u4ee5\u77e5\u9053
p(x=0)=(1-p)^2
\u90a3\u4e48\u6709\u7b49\u5f0f4/9=(1-p)^2
p\u5c5e\u4e8e[0,1]\u8fd9\u4e2a\u533a\u95f4\uff0c\u6240\u4ee5p\u7684\u552f\u4e00\u89e3\u662f1/3
e(x)=2*(1/3)=2/3
\u5e0c\u671b\u53ef\u4ee5\u5e2e\u52a9\u5230\u4f60\uff0c\u5982\u679c\u8fd8\u6709\u95ee\u9898\u518d\u95ee\u6211\u5427
\u671b\u91c7\u7eb3
P(Y≥1)=1-(1-p)^3=26/27
(2)np 乘(1-p)^{n-1}= n(n-1)/2 乘p^2 乘(1-p)^{n-2}=2乘n(n-1)(n-2)/6乘p^3乘(1-p)^{n-3}
解得n=5, p=1/3
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绛旓細闅忔満鍙橀噺X鏈嶄粠浜岄」鍒嗗竷.鍏跺垎甯冨垪涓猴細X 0 1 2 P (1-p)² p(1-p) p²P(x=0)=(1-p)²P(X=1)=C(2,1)P(1-p)P(X=2)=p².EX=np=2p.DX=np(1-p)=2p(1-p).
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绛旓細鎭╋紵 浣犱笉鎳傦紵X锝B锛2锛宲)琛ㄧず闅忔満鍙橀噺X鏈嶄粠浜岄」鍒嗗竷锛屼笖鎿嶄綔娆℃暟涓2锛屾瘡娆℃垚鍔熺殑姒傜巼涓簆 鍥犱负鍙搷浣2娆★紝鎵浠ユ渶澶氳兘鎴愬姛2娆 P(X澶т簬绛変簬1锛=p^2+2p(1-p)=5/9锛堝鏋滆鏄簲鍒嗕箣涔濋偅鏄棤瑙ｇ殑锛夎В寰梡=1/3 鍥犱负Y鐨勫彂鐢熸鐜囦篃鏄痯锛屽氨鍙互鐢ㄤ簩椤瑰垎甯冨叕寮忔眰鍑 P(Y澶т簬绛変簬1锛=1-锛1-...
绛旓細x锝B(2锛0.5)鍗x鏈嶄粠浜岄」鍒嗗竷 閭ｄ箞x鐨勫彇鍊煎彧鑳芥槸0锛1锛2 鎵浠(x鈮1)= 1 -P(x=0)鑰孭(x=0)=0.5*0.5=0.25 鎵浠 P(x鈮1)=1 -P(x=0)=1 -0.25=0.75
绛旓細鍥犱负X~B(n,p),鎵浠(X)=np,D(X)=np(1-p)鍙圖(X)=E(X^2)-E(X)^2,鏁匛(Y)=E(X^2)=np(1-p)+(np)^2
绛旓細鍥犱负X~B(n,p)锛屾墍浠(X)=np锛孌(X)=np(1-p)鍙圖(X)=E(X^2)-E(X)^2锛屾晠E(Y)=E(X^2)=np(1-p)+(np)^2
绛旓細璇︾粏杩囩▼濡傚浘rt锛屽笇鏈涜兘甯埌浣犺В鍐抽棶棰
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绛旓細cov(x,y)=cov(x,2x+3)=cov(x,2x)+cov(x,3)=2D(X)=2np(1-p)=2*100*0.6*0.4=48 娉2锛歝ov(x,y)=E(XY)-EXEY=E(2X*X+3X)-EX(2EX+3)EX=np=60,DX=np(1-p)=24 E(X*X)=3624 cov(x,y)=2*3624+3*60-60*123=48 ...
