Question 9 An integer x between 1 and 10 (included) will be drawn at random following a uniform distribution. There is thus one chance out of ten that x = 1, one chance out of ten that x = 2, etc. Inspired by the television show "The Price is Right," the game starts with Player 1 proposing an integer between 1 and 10 (included). After observing 1's chosen integer, Player 2 herself chooses an integer between 1 and 10 (included). Then x is revealed, and the player closest to x **and** below x wins a prize of $1,000. Ties are broken by flipping a fair coin to decide who wins the prize. Each player's goal is to maximize his or her probability of winning. (a) (2 points) For each of the ten possible integers that Player 1 might pick, compute Player 2's best response. (b) (1 point) Given (a), what is the best integer that Player 1 can pick?