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.

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4. a1. vince owns a television repair shop that is insured undera commercial package policy. the policy includes thebuilding and personal property coverage form and thecauses-of-loss broad form. the declarations page indicatesthat coverage applies to both the building and the namedinsured's business property. explain whether or not thefollowing losses would be covered under his policy.a. a fire occurs on the premises, and the building isbadly damaged.b. a burglar steals some money and securities from anunlocked safe.c. a business computer is damaged by vandals whobreak into the shop after business hours.d. a tornado touches down near the store. several tel-evision sets of customers in the shop for repair aredamaged in the storm.til

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