A computer program can make calls to two subroutines, A and B. In a randomly chosen run, let X be the number of calls to subroutine A and let Y denote the number of calls to subroutine B. The joint probability mass function of X and Y is given in the following table.
|
y
|
|
x
|
1
|
2
|
3
|
|
1
|
0.15
|
0.10
|
0.10
|
|
2
|
0.10
|
0.20
|
0.15
|
|
3
|
0.05
|
0.05
|
0.10
|
a. Find the conditional probability mass function Px|y(y|2)
b. Find the conditional expectation of E(Y|X =2)
c. Find the correlation coefficient between X and Y. (Show all solution steps).