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, one-fifth 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 otherwise 0 if professor is away from the office otherwise

(a) Find the joint probability function of X and Y.

(b) Find the conditional probability function of Y. given X = 0.

(c) Find the marginal probability functions of X and Y.

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