5. After watching a number of children playing games in a video arcade, a statistics practitioner estimated the following probability distribution of X, the number of games per visit. 1 3 4 f(x) 0.05 0.2 0.3 0.25 0.2 (a) What is the probability that a child will play at most three games? (b) What is the mean and variance of the number of games played? (c) Suppose that each game costs $2 to play. Use the laws of expected value and variance to determine the expected value and variance of the revenue (the amount of money) the arcade receives per child.

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