Assignment:
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
Provide complete and step by step solution for the question and show calculations and use formulas.