In: Statistics and Probability
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. Hint: what is the
probability that any car not turning west will turn east?
(b) Find the joint distribution of X and Y. Be careful with the
limits of validity.