4.81 A college bookseller makes calls at the offices of professors and forms the impression that professors are more likely to be away from their offices on Friday than any other working day. A review of the records of calls, 1/5 of which are on Fridays, indicates that for 16%

of Friday calls, the professor is away from the office, while this occurs for only 12% of calls on every other working day. Define the random variables as follows:

X = 1 if call is made on a Friday X = 0 otherwise Y = 1 if professor is away from the office Y = 0 otherwise

a. Find the joint probability distribution of X and Y.

b. Find the conditional probability distribution of Y, given X = 0.

c. Find the marginal probability distributions of X and Y.

d. Find and interpret the covariance between X and Y.