# Math Help - Basic expectation question

1. ## Basic expectation question

Assign a value of 1 point to an Ace, 11 points to Jack, 12 to a Queen, and 13 for a King. The numbered cards (2-10) are assigned the value shown on the card.

Draw 2 cards with replacement.

Let X be the value of the first card, and let Y be the value of the second card. What is E(X+Y)? StdDev(X+Y)?

Is it E(X+Y) = E(X) + E(Y) = 14?

E[(X+Y)^2] = ??

Also, is the distribution of X, P(X=x ) = 4/52?

Thanks !

2. P(X=k)=1/13 for k=1,2,3... 13 same for Y.
They are indep.

So compute $E(X)$ and $E(X^2)$....

By indep, since you are sampling wr, we have V(X+Y)=V(X)+V(Y)