1. A random variable X has expected value and probability distribution as follows: X -3 -2 - 1 0 W N f (X) a 2a b 10 (a) Find the values of a and b. ( b ) Find E[X2 + 1]. (8 marks) 2. Suppose that you are looking for a student at your college who lives within five miles of you. You know that 55% of the 25,000 students do live within five miles of you. You randomly contact students from the college until one says he or she lives within five miles of you. (a) What is the probability that you need to contact four people? (b) How many students from the college you expect to contact until you find one lives within five miles of you? (c) What is the standard deviation of the number of students to be contacted until one says who lives within five miles of you? (d) Suppose you randomly ask 5 students at your college, what is the probability that 3 of them live within five miles of you? (e) Suppose you randomly ask 5 students at your college, what is the expected number of students who live within five miles of you? (7 marks)