Problem Set due Jun 29, 2021 16:59 MST Problem 7. Sum of a random number of r.v.'s 2 points possible (graded) A fair coin is flipped independently until the first Heads is observed. Let the random variable / be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, so that the first head is observed after 4 tosses, then K = 4+ 1 = 5. For k = 1, 2, ..., K, let Xx be a continuous random variable that is uniform over the interval 0, 5). The Xx are independent of one another and of the coin flips. Let X = _ Xx. Find the mean and variance of X. You may use the fact that the mean and variance of a geometric random variable with parameter p are 1/p and (1 - p) /p2, respectively. E[X] Var (X) =