Originally Posted by

**Danneedshelp** 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 $\displaystyle V (Y ) = V (X )$ and expanded the the variance formula to include $\displaystyle E(Y^{2})-E(Y)^{2}=E(X^{2})-E(X)^{2}$, 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 $\displaystyle P(Y= -1)=1/4$, $\displaystyle P (Y = 0) = 1/4$,

$\displaystyle P (Y = 1) = 1/4$, and $\displaystyle P (Y = 2) = 1/4$. Consider the discrete random variable X having

$\displaystyle P (X =

-1) = p_{1}$ , $\displaystyle P (X = 0) = p_{2}$ , $\displaystyle P (X = 1) = p_{3}$ , and $\displaystyle P (X = 2) = p_{4}$ . Also, suppose

p2 = 2p1 . Find p1 , p2 , p3 , and p4 such that $\displaystyle E(Y ) = E(X )$ and $\displaystyle V (Y ) = V (X )$.

Any help would be much appreciated, thanks