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:
Y=0 Y=1 Y=2
X=0 0.10 0.11 0.05
X=1 0.23 0.17 0.08
X=2 0.08 0.10
a) What is the value of Pr(X=2,Y=1)
b) Find Pr(X < 1)
c) Find Pr(Y ? 1)
d) Find the probability that the standard for ozone is exceeded at least once.
e) Find the probability that the standard for particulate matter is never exceeded.
f) Find the marginal probability mass function Pr(X).
g) Find the marginal probability mass function Pr(Y).
h) Find the expected value of X, E[X].
i) Find the expected value of Y, E[y].