f(x)=P(X=x)=1/4(当x=1,2,3,4) f(x)=0(当x不等于1,2,3,4)
f(y) = 1/4(当y = 0,2) f(y) = 1/2 (当y = 1) f(y) = 0(当y不等于0,1,2)
令Z=XY, f(z) = 1/4 (当z=0) f(z) = 1/8 (当z=1,3) f(z) = 1/16 (当z=6,8) f(z) = 3/16 (当z=2,4)
证明f(xy)不等于f(x)f(y) 只需要一个反例,取x=1,y=0,则z=0,f(x)=1/4,f(y)=1/4得到f(x)f(y)=1/16,但是f(xy)=f(z)=1/4,1/16不等于1/4,得证.
当X=2的时候Y=1所以: P(y|x=2) = 1(当y=1) P(y|x=2) = 0(当y不等于1)