Let x∼ Exponential (mean =lambda ) and (Y|x=x)∼ Uniform (0,x).
(a) 5pts Find f_(Y)(y), the probability density function of Y and show that int_(-infty )^(infty ) f_(Y)(y)dy=
1 .
(b) 5pts Find V(Y).
(c) [5 pts] Find f(x|y), the conditional density of x given Y=y, and show that
int_(-infty )^(infty ) f(x|y)dx=1.
(d) [5 pts] Find E(x|Y).
7. Let X ~ Exponential (mean = X) and (Y|X = x) ~ Uniform (0,x)
(a) [5 pts] Find fy(y), the probability density function of Y and show that J-o fy(y)dy =
1.
(b)[5 pts] Find V(Y).
f-m f(x|y)dx =1.
(d)[5 pts] Find E(X|Y)
