John and Two of His Friends Have One-On-One Basketball Tournaments

Essay

John and two of his friends have one-on-one basketball tournaments almost every week. Each person plays each other person once. Let X be the number of games that John wins next week X. Based on the results of the games over the past year, John constructs the following probability distribution for X.

Find
(a) The expected number of wins.
(b) The standard deviation of the number of wins.
(c) Explain how John should use the results of previous games to construct the tabled probability distribution.