Let X, Y, and Z be independent random variables whose distributions are given by:
X ~ Bin(25, 0.75),
Y ~ Geo(0.5),
Z ~ Po(5).
a. Plot the probability mass functions outlined above in ONE figure with three subplots, using the same x-axis range for all of the subplots.
b. Find a combination of X, Y and Z whose expectation is e^2 and whose variance is sqrt(pi).
c. Find a combination of X, Y and Z whose expectation is equal to the variance.
d. Compute the covariance of the resulting variable in part (c) with Z.