At a certain intersection, of all cars traveling north, the relative frequency of cars continuing in the same direction is p. The relative frequency of those turning east is q; all others turn west. Assume that drivers behave independently of one another. A small group of n cars enters the intersection. For this group
(a) What is the marginal distribution of Y, the number of cars turning west? Find the conditional distribution of X, the number of cars turning east, given that Y equals y.
(b) Find the joint distribution of X and Y. Be careful with the limits of validity. (X, Y, and Z, the number going straight, have a joint "multinomial" distribution which is studied in Sec. 3.6.1.)