The card game Hearts is played with a standard 52-card deck. There are 13 hearts in the deck, each of which is worth 1 point. There is also one card called the Queen of Spades in the deck, which is worth 13 points. You draw a hand of 13 cards (without replacement). (a) The number of hearts you draw follows a Hypergeometric distribution. What is its expected value?(b) The number of Queens of Spades is, of course, either 0 or 1 (since there’s only one in the deck), so it follows a Bernoulli distribution. What is its expected value? (c) What is the expected value of the total number of points in the hand you draw?

Question

. The card game Hearts is played with a standard 52-card deck. There are 13 hearts in the
deck, each of which is worth 1 point. There is also one card called the Queen of Spades in
the deck, which is worth 13 points.
You draw a hand of 13 cards (without replacement).
(a) The number of hearts you draw follows a Hypergeometric distribution. What is its
expected value?(b) The number of Queens of Spades is, of course, either 0 or 1 (since there’s only one in
the deck), so it follows a Bernoulli distribution. What is its expected value?
(c) What is the expected value of the total number of points in the hand you draw?