Toss three fair coins. Let X be the random variable that uses the rule of assignment:
(2 × number of tails) − number of heads. For example if the outcome is TTH then X(TTH) =
2 ×2 −1 = 3. Determine each of the following:
a. The sample space, S.
b. The range of X?
c. The CDF of X.
d. The PMF of X.
e. The expected value of X.
f. The variance and standard deviation of X