14. Let X be the proportion of customers of an insurance company who bundle their auto and...

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14. Let X be the proportion of customers of an insurance company who bundle their auto and home insurance policies. Let Y be the proportion of customers who insure at least their car with the insurance company. An actuary has discovered that for, 0 ≤ x ≤ y ≤ 1, the joint distribution function of X and Y is F(x, y) = x(y2 + xy − x2). Find the expected value of the proportion of the customers of the insurance company who bundle their auto and home insurance policies.

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