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In: Statistics and Probability

At a certain intersection, of all cars traveling north, the relative frequency of cars continuing in...

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.

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