Question

We have two random variables X and Y. P( X = .25 ) = .25 , P(X = .5 ) = .5 , and the P( X = .75 ) = .25

Suppose Y is a Bernoulli Random Variable and the Joint Distribution of X and Y satisfies condiiton that E[Y|X] = X^2

Help me calculate E[XY] & E[Y/X] & E[X|Y]

I imagine we start by calculating E[X] which i got as .5, then calculate E[X^2] as 9/32 since we can rationalize that E[E[Y|X] == E[x^2] == 9/32 == E[Y] which gives us E[Y]. THough after this, we'll need to find E[XY] which equals Cov(X,Y) + E[x]*E[Y] , I can't figure out how to find the Covariance or how to test if these are independent.  

Answer 1

Soluton suppose x and y are random vanob les Geuh that p(X 0.25)=0.25 , In19 y ís Bernoulli random vanable suh hat E(%):x2 cons ider