Refer to Exercise 1.

a. Find the conditional probability mass function p_{Y |X} (y |0).

b. Find the conditional probability mass function p_X|Y (x |1).

c. Find the conditional expectation E(Y | X = 0).

d. Find the conditional expectation E(X | Y = 1).

Refer to Exercise 1.

In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table:

0.10 0.11 0.05 0.17 0.23 0.08 0.06 0.14 0.06