An insurance company sells both homeowners’ insurance and

QUESTION:

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:

\(\begin{aligned}&P(X=500), P(Y=500), P(Y=500 \mid X=500), \\&P(Y=100 \mid X=500) .

\end{aligned}\)

(b) Compute the means \(\mu_{X}, \mu_{Y}\), and the variances \(\sigma_{X}^{2}\), \(\sigma_{Y}^{2}\).

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

(d) Compute \(\operatorname{Cov}(X, Y)\).

(e) Find the correlation coefficient, \(\rho\).

Equation Transcription:

Text Transcription:

X  

Y  

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

E(X | Y = 100), E(Y | X = 500)  

Cov(X, Y)

rho