We consider two random variables X and Y with simultaneous probability distributionp(x,y)=P(X=xY=y) given by this table:

x/y	0	1	2
0	0.05	0.25	0.1
1	0.1	0.05	0.1
2	0.25	0	0.1

a) Find the marginal probability distributions for X and Y. What isP(X=2Y=2)? Is X and Y independent random variables? Justify the answer.

b) Find the correlation between X and Y when you know the expectations are E(X)=0.95 and E(Y)=0.9, and the variace V(X)=0.747 and V(Y)=0.69.

c) Find conditional expectation E(Y|X = 2) and the conditional variance V(Y|X = 2)