1. (10 points) Pat is taking an economics course. Pat's exam strategy is to rely on luck for the next exam. The exam consists of n multiple-choice questions. Each question has five possible answers, only one of which is correct. Pat plans to guess the answer to each question without reading it. If a grade on the exam is more than 50%, Pat will pass the exam. Find the probability that Pat will pass the exam. (a) Find the probability that Pat will pass the exam when n = 2. (b) Find the probability that Pat will pass the exam when n = 7. 2. (25 points) After analyzing several months of sales data, the owner of an appliance store produced the following joint probability distribution of the number of refrigerators and stoves sold daily. Let X denote the refrigerators that will be sold in a day and let Y denote the number of stoves to be sold in a day. An analysis of their past daily performances has the following joint probabilities X =0 X=1 Y =0 0.3 0.4 Y =1 0.2 0.1 (a) Find E (X) , E( Y). (b) Find V (X) , V (Y) . (c) Find Cov (X, Y) , Corr (X, Y) . (d) Find E ( X + Y) , V (X + Y). (e) Find the conditional means, E(Y X = 0) and E(Y|X = 1)