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 .
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 .