Question

设二维随机变量(X,Y)的分布律为

Answer 1

P{Y=1|X=0}=1/2-->P{Y=1,X=0}/P{X=0}=b/P{X=0}=1/2,P{X=0}=a+b-->b/(a+b)=1/2

P{X=1|Y=0}=1/3-->P{X=1,Y=0}/P{Y=0}=c/P{Y=0}=1/3,P{Y=0}=a+c-->c/(a+c)=1/3

a+b+c+0.5=1

-->a=b=2c-->a=b=0.2,c=0.1