Assume we flip a fair coin twice, independently of each other. Define the following random variables:
X = the number of heads,
Y = the number of tails,
Z = the number of heads times the number of tails.
(a) Determine the expected values of these three random variables.
(b) Are X and Y independent random variables?
(c) Are X and Z independent random variables?
(d) Are Y and Z independent random variables?