# Question: An insurance company sells both homeowners insurance and automobile deductible

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.

(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.

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