**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 be the time (in hours) of his flight from City A to City B. Let be the time (in hours) of the bus ride. The following is the joint density function of and .

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

**Problem 31B**

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

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

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**Answers**

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