已知随机变量X服从二项分布，X～B（4，二分之一），则P（X=1）的值为多少
\u8bbe\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u4e8c\u9879\u5206\u5e03b(2,p),\u968f\u673a\u53d8\u91cfY\u670d\u4ece\u4e8c\u9879\u5206\u5e03b(3,p)\uff0c\u82e5P(X\u22651)=5/9,\u5219P(Y\u22651)=?(1)\u7531P(X\u22651)=5/9\uff0c\u53ef\u5f97P(X=0)=4/9=(1-p)^2,\u6545p=1/3,\u4ece\u800c
P(Y\u22651)=1-(1-p)^3=26/27
(2)np \u4e58(1-p)^{n-1}= n(n-1)/2 \u4e58p^2 \u4e58(1-p)^{n-2}=2\u4e58n(n-1)(n-2)/6\u4e58p^3\u4e58(1-p)^{n-3}
\u89e3\u5f97n=5, p=1/3
np=2.4 (1)
np(1-p)=1.44 (2)
1-p=1.44/2.4=0.6 p=0.4 n=2.4/0.4=6
\u7b54\u6848\uff1aB. n=6\uff0cp=0.4\u3002
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绛旓細銆愮瓟妗堛戯細B
绛旓細銆愮瓟妗堛戯細B
绛旓細鈭闅忔満鍙橀噺X鏈嶄粠浜岄」鍒嗗竷X锝濨锛坣锛宲锛夛紝涓擡锛圶锛=3锛孌锛圶锛=2锛屸埓E锛圶锛=3=np锛屸憼D锛圶锛=2=np锛1-p锛夛紝鈶♀憼涓庘憽鐩搁櫎鍙緱1-p= 2 3 锛屸埓p= 1 3 锛宯=9锛庢晠閫塀锛
绛旓細D
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绛旓細EX=10*0.1=1 DX=10*0.1*(1-0.1)=0.9
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np=2.4 (1)np(1-p)=1.44 (2)1-p=1.44/2.4=0.6 p=0.4 n=2.4/0.4=6 绛旀锛欱. n=6锛宲=0.4銆
