Problem 3. (15 points) You are selling your bike. You get offers one by one. You have decided to stop and accept an offer as soon as you see one which is better than the first offer you got. (You always skip the first offer). What is the expected number of offers you will to wait for, including the first one, until you accept an offer? Mathematically, let's model this process as follows. Let X1, X2, ... denote an infinite sequence of independent uniformly-distributed random samples from the interval [0,1]. (Interpretation: X; is the ith offer.) Let 7 be the smallest i > 1 such that X; > X1. What is E[r]? Hint: Use following formula for expected value of a non-negative integer valued random variable 2: E[2] - Pr(Z >n).