3,54 Consider an insurance agency with 15.000 customers who have both auto and homeowners policies. Let X and Y be discrete r.v.'s. where X = the deductible amount on the auto policy and Y: the deductible amount on the homeowner policy. A summary of these policies is shown below. Number of Customers Y (Home Policy Deductible) $0 $100 $200 5100 X (Auto Policy Deductible) $250 3750 3750 7500 (I) Find the marginal p.m.f.'s of X and Y. Are X and Y statistically independent? (b) Find the conditional distribution of Y given X . (c) Find the covariance of X and Y