## Joint Probability/Marginal Probability

1. 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-…fth 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. De…ne 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 function of X and Y .
b. Find the conditional probability function of Y given X = 0.
c. Find the marginal probability functions for X and Y .
d. Find and interpret the covariance between X and Y .

Am I doing this right?

For part a I did that P(x and y) = P(x)*P(y)=(.2*.16)=.032

For part b i did P(Y=y|X=0)=.12

Part C P(x)=Sum(P(x,y),y) = .032+4*.2*.12=.128 and same for x.

Is that right? If not what am I doing wrong and what should I do?? Thanks