Question: David is an insurance broker who believes that the probability of making a sale is 0.3.
(a) Find the mean and variance of a random variable defined to be 1 it he makes a sale and 0 otherwise.
(b) What is p and 1 - p? Check that the probability distribution satisfies the two conditions discussed in class.
(c) Suppose now David has 5 contracts and now the probability of making a sale is 0.4. Compute the probability that he makes:
i. at most one sale,
ii. between 2 and 4 sales.
(d) Graph the distribution function checking that the probabilities are between 0 and 1 for all x, and that the sum of the probabilities is equal to 1.