The runner-up in a road race is given a reward that depends on the difference between his time and the winners time. he is given 10 dollars for being one minute behind, 6 dollars for being one to three minutes behind, 2 dollars for being 3 to 6 minutes behind, and nothing otherwise. given that the difference between his time and the winner’s time is uniformly distributed between 0 and 12 minutes, find the mean and variance of the reward of the runner-up.