Chapter 4.3, Problem 6E

An insurance company sells both homeowners’ insurance and automobile deductible insurance. Let X be the deductible on the homeowners’ insurance and Y the deductible on automobile insurance. Among those who take both types of insurance with this company, we find the following probabilities:

(a) Compute the following probabilities: $P\left(X=500\right),P\left(Y=500\right),P\left(Y=500|X=500\right),P\left(Y=100|X=500\right)$.

(b) Compute the means and the variances a, 4

(c) Compute the conditional means $E\left(X|Y=100\right),E\left(Y|X=500\right)$.

(d) Compute Cov(X, Y).

(c) Compute the correlation coefficient $\rho =\frac{\mathrm{cov}\left(X,Y\right)}{{\sigma }_X{\sigma }_Y}$.