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(X = 500), P(Y = 500), P(Y = 500 |X = 500), P(Y = 100 |X = 500).

(b) Compute the means μX, μY, and the variances σ2X,σ2Y .

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

(d) Compute Cov(X,Y).

(e) Find the correlation coefficient, ρ.

Step1 of 6:

Given that X denotes the insurance deductible insurance on the homeowners’ insurance and Y denotes the deductible insurance on automobile insurance. The corresponding probabilities are given.

We have to find the required probabilities using the given probabilities.