# Exam P Practice Problem 31 – Covariance

Problem 31A

A traveler is at the airport of City A and wants to reach his home in City B. He plans to take an airplane flight from City A to the airport of City B. Once he arrives in the airport of City B, he plans to reach his home by riding in a bus. Let $X$ be the time (in hours) of his flight from City A to City B. Let $Y$ be the time (in hours) of the bus ride. The following is the joint density function of $X$ and $Y$.

$\displaystyle f(x,y)=\frac{1}{16} \ x \ y \ \ \ \ \ \ \ 0

Let $W$ be the total time of travel from the airport of City A to his home in City B. Calculate the covariance of $X$ and $W$.

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Problem 31B

An investor is facing two potential financial losses $X$ and $Y$ with the following joint density function:

$\displaystyle f(x,y)=0.025 \ x \ e^{-0.2 \ y} \ \ \ \ \ \ \ 0

Let $T$ be the total of these two losses. Calculate the covariance of $T$ and $Y$.

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