1. Aaron is a quarterback from Chico, CA who just started playing for the Green Bay Packers. Being new to Wisconsin, and being from northern California where the seasons make sense, Aaron naively assumes that November if fall. So he believes that for a random day in November, the probability it is cold is 20%, the probability it is warm is 70%, and the probability it is hot is 10%. (a) What does Aaron believe is the probability of having 5 straight cold days in November? (Assume independence) After arriving and experiencing some really cold weather, Aaron starts to wonder if maybe the seasons work differently in Wisconsin. He still thinks November is fall with 90% condence, but acknowledges a 10% chance that somehow November is the dead of winter in Wisconsin. In the winter, still thinking of CA, Aaron believes the probability of a hot day is 0%, the probability of a warm day is 30%, and the probability of a cold day is 70%. Over the next 5 days, Aaron observes cold, warm, cold, cold, warm. (b) Assume the days are independent. What does Aaron believe is the probability that it is actually fall in November in Wisconsin? (0) Aaron gets hit in the head a lot, so now suppose he suffers from law of small num bers bias. He believes days are \"drawn from an urn\" of 10 days with replacement only after 5 days. What is the probability it is actually fall