Problem 10: consider a simple online auction system working as follows. there are n bidding agents; agent i has a bid bi which is a positive natural number. assume that all bids are distinct. the bidding agents appear in an order chosen uniformly at random, each proposes its bid bi in turn and at all times the system maintains a variable b ∗ equal to the highest bid seen so far (starting with b ∗ = 0 initially). what is the expected number of times b ∗ is updated when this process is executed, as a function of the parameters in the problem? example suppose b1 = 20, b2 = 25 and b3 = 10 and bidders arrive in the order 1, 3, 2. then b ∗ is updated for 1 and 2 but not for 3.