设随机变量X~b(3,0.4),求Y=X²-2X的分布率
\u8bbe\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u4e8c\u9879\u5206\u5e03B\uff083,0.4\uff09\uff0c\u6c42\u968f\u673a\u53d8\u91cfY=X(X-2\uff09\u7684\u6982\u7387\u5206\u5e03X\u670d\u4eceB(3,0.4)\uff0c\u6545X\u53ef\u53d6\u503c\u4e3a0\uff0c1,2,3
\u5f53X=0\u65f6\uff0cY=0
\u5f53X=1,Y=-1
\u5f53X=2\uff0cY=0
\u5f53X=3\uff0cY=3
\u6240\u4ee5\uff0cY\u662f\u4e2a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\uff0c\u53ef\u53d6\u7684\u503c\u4e3a-1,0,3
P\uff08Y=-1\uff09=P(X=1)=C(3,1)(0.3)^1*(0.7)^2=0.441
P\uff08Y=0\uff09=P\uff08X=0)+P\uff08X=2\uff09=0.343+0.189=0.532
P\uff08Y=3)=P(X=3)=0.027
\u8fd9\u6837\u5c31\u53ef\u4ee5\u5f97\u5230Y\u7684\u5206\u5e03\u5217\u4e86
E(X²)=D(X)+E²(X)=3+3*3=30
E(Y²)=D(Y)+E²(Y)=1.6+4=5.6
E(2X^2-Y^2)=2E(X²)-E(Y²)==54.4
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P{Y=-1}=P{X=1}=C_3^1(0.4)^1(0.6)^2
P{Y=3}=P{X=3}=C_3^3(0.4)^3(0.6)^0
P{Y=0}=1-P{Y=-1}-P{Y=3}
绛旓細X~B(3,0.4)锛屽垯P(X=1)=C(3,1)(0.4)(0.6^2)=0.432 P(X鈮1)=1-P(X=0)=1-C(2 0)*(p^0)(1-p)^2=1-(1-p)^2=3/4 p=1/2 p(y鈮1)=1-P(Y=0)=1-C(3 0)*(p^0)(1-p)^3=7/8
绛旓細E(X)=3脳0.4=1.2 E(Y)=3/2-1/2路E(X)=1.5-0.6=0.9 銆愰檮娉ㄣ戯紙1锛塜~B(n锛宲)锛屽垯 E(X)=np 锛2锛塃(kX+b)=kE(X)+b
绛旓細浜岄」鍒嗗竷锛孍x=3*0.4=1.2锛
绛旓細E(X)=3脳0.4=1.2 E(Y)=3/2-1/2路E(X)=1.5-0.6=0.9 銆愰檮娉ㄣ戯紙1锛塜~B(n,p),鍒 E(X)=np 锛2锛塃(kX+b)=kE(X)+b
绛旓細X鏈嶄粠鍙傛暟涓3,0.4鐨凚ernoulli鍒嗗竷 鍗冲湪3娆$嫭绔嬮噸澶嶈瘯楠屼腑,姣忔璇曢獙鎴愬姛鐨勬鐜囦负0.4,鎬荤殑鎴愬姛娆℃暟涓篨鐨勫垎甯 P(X=k)=C(3,k)*0.4^k*0.6^(3-k)
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