Suppose that the monthly sales of a dealer of a certain luxury car constitute a conditional Poisson process such that A is a discrete random variable taking the values 2, 3, or 4, with probabilities 1/4, 1/2, and 1/4, respectively.
(a) If the dealer has three cars of this type in stock, what is the probability that the three cars will be sold in less than a month?
(b) Suppose that A = 3. Calculate V[M | M M is the number of cars sold in one month.