In: Statistics and Probability
Suppose that the Dongguk football team plays twelve games in a season. In each game, they have a1/3 probability of winning, a 1/2 probability of losing, and a 1/6 probability of tying. The outcome of each game is independent of all others. [1] What is the probability that the team will end the season with a record of (7 wins, 3 losses, 2 ties)? [2] Suppose that for each win, the team receives three points, and for each tie they receive one point. Let X be a random variable that denotes the number of points the team has earned after four games. Calculate the probability mass function of X