Pick two cards. Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously, i.e., grab two cards at (once-so they are not the same card!). There are 12 cards which are considered !face cards (4 Jacks, 4 Queens, 4 Kings). There are 4 cards with the value 10. Let X be the number of face cards in your hand; let Y be the number of 10's in your hand.
a. Before looking at the cards, put one in your left hand and one in your right hand. Let X1 and X2 indicate, respectively, whether the cards in your left and right hands (respectively) are face cards. Then X = X1 + X2. Find the expected value of X by finding the expected value of the sum of the indicator random variables.
b. Before looking at the cards, put one in your left hand and one in your right hand. Let X1 and X2 indicate, respectively, whether the cards in your left and right hands (respectively) are 10's. Then X = X1 + X2. Find the expected value of X by finding the expected value of the sum of the indicator random variables.