1. [6 marks] An automobile salesman estimates that the number of automobiles X sold each week follows the following probability distribution: Number of automobiles sold per week Probability 0 0,06 1 0,13 2 3 4 0,37 0,25 0,19 a) b) If his weekly salary Y is $50 plus a commission of $100 per automobile sold, what weekly salary can he expect? [1.5 mark] Suppose that the profit from the sale of automobiles is a random variable U given by the function U 10X240. Find the expected weekly profit. [1.5 mark] c) The car seller also sells trucks. According to the estimated number of trucks sold each week is a random variable V whose probability distribution is given by the table: Number of automobiles sold per week Probability 0 1 2 0,30 0,55 0,08 0,05 0,02 d) 3 4 How many vehicles (cars and trucks) can he expect to sell in any given week? [1.5 mark] We assume that the random variables X and V are independent, calculate the variance of Y+V. [1.5 mark] 2. [6 marks] The operating time of a computer before its first failure is a continuous random variable whose probability density function is given by: ce f(x) = 100, if x0 0, if x