Problem 1 say X is a non-negative rv, that P(X≥0)=1. Prove: EX=0 iff P(X=0)=1
Problem 2
Say (X,Y) is a bivariate r.v. with joint pdf f(x,y) = cx if 0<x<y<1, 0 otherwise
1) Find c
2) Find the marginals pdf's fX and fY 3) Find the conditional pdf's fX|Y=y and fY|X=x 4) Find the conditional expectations E[X|Y=y] and E[Y|X=x]
5) Show that E[E[X|Y]] = E[X] and E[E[Y|X]] = E[Y]