Problem 6.4. The number of insurance policies a salesman will sellon anyone day is denoted by the random variable X and has the following probability distribution: k 0 1 2 P(X = k) 0.4 0.2 0.3 0.1 (a) Find the probability that on a randomly selected day he will sell at least one policy. (b) Find the expected value of X, i.e. E(X). (c) If the salesman makes $800 on each policy sold, find his expected earnings. Hint: His earnings are given by the random variable Y = 800. X. You are being asked to compute E(Y). (d) Find the probability the salesman will make more than $1500 on any given day. Hint: First find the distribution of Y. Problem 6.5. Suppose: X ~ Binomial(4, ?). Compute P(X 2 3), P(X = 4X > 3), and P(X 2 3|X = 4). Hint: For the latter, it is not necessary to use Bayes' rule: just employ the definition of conditional probability