The number of cars being repaired at a small repair shop has the following PMF: Each car

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The number of cars being repaired at a small repair shop has the following PMF:PN(n)= 000 2 0 for n = 0 for n = 1 for n = 2 for n = 3 otherwise

Each car that is being repaired is a four-door car with probability 3/4 and a two door car with probability 1/4, independently from other cars and independently from the number of cars being repaired. Let X be the number of four-door cars and Y be the number of two-door cars currently being repaired.

a. Find the marginal PMFs of X and Y.

b. Find the joint PMF of X and Y.

c. Are X and Y independent?

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