I am stuck on the below problem. I am not sure how to approach. What I have done so far is used the fact that

and expanded the the variance formula to include

, but I have not had much luck with it. I also thought about settin gup a system, but I am not sure how I would do that.

Q: Suppose Y is a discrete random variable having

,

,

, and

. Consider the discrete random variable X having

,

,

, and

. Also, suppose

p2 = 2p1 . Find p1 , p2 , p3 , and p4 such that

and

.

Any help would be much appreciated, thanks