Xの確率分布は 6Cx(1/3)^x/(2/3)^(6-x) x=0,1,2,3,4,5,6 Yの確率分布は 3Cy(1/2)^y/(1/2)^(3-y)=3Cy(1/2)^3 y=0,1,2,3
Z=XY=4となるのは (X,Y)=(2,2),(4,1)でXとYは独立なので
P(Z=4)=P(X=2)P(Y=2)+P(X=4)P(Y=1) =6C2(1/3)^2/(2/3)^4・3C2(1/2)^3+6C4(1/3)^4/(2/3)^2・3C1(1/2)^3 =25/162
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