Problem 20.34. There are n elderly couples and m randomly selected people expire. What is the expected number of remaining couples. [Hint: Xi = 1 if both members of couple i remain.]Problem 21.39. 100 people toss their hats up. The hats land randomly on heads. Let the random variabls X be the number of people who get their hats back. (a) Compute 1E[X] and var[X]. [Hint: Let X,- = 1 if person 2' gets their hat back and X,- = 0 otherwise. How is X related to the X1- .7 Are the X,- independent7] (b) Give an upper bound on the probability that more than half the people get their hats back