Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for
i >= 0, j >= 0, and i + j < 4. Determine

a) the marginal probability mass function of X

b) the probability mass function of Y

c) the conditional probability mass function of X given Y = 0

d) the probability mass function of Z = X + Y

e) the conditional probability mass function of Z given X = 0

f) the mean of X

g) the expected value of Y

h) the mean of Z

i) the variance of X

j) the variance of Y

k) the variance of Z

l) the mean of XY

m) the covariance of X and Y

n) the mean of X conditioned on Y=0