From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 73. Consider an insurance agency with 15,000 customers who have both auto and homeowners policies. Let X and Y be discrete random variables, where X the deductible amount on the auto policy and Y the deductible amount on the homeowner policy. A summary of the number of customers with these policies is shown below. = Home Policy Deductible (Y) Total
$0 $100 $200
Auto Policy $100 3000 1500 3000 7500
Deductible (X) $250 750 2250 4500 7500
Total 3750 3750 7500 15,000
a) Find the marginal pmf of X and Y. Are X and Y independent?
b) Find the conditional distribution of Y, given X = 100.
c) Find the conditional distribution of Y, given X = 250.
d) Find the covariance of X and Y.
e) Determine the correlation coefficient between X and Y.