A fair coin (i.e., heads and tails are equally likely) is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.
a. Find the probability distribution of X.
b. Find the probability that two or fewer heads are observed in three tosses.
c. Find the probability that at least one head is observed in three tosses.
d. Find the expected value of X.
e. Find the standard deviation of X.