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Wayne Gretsky scored a Poisson mean 6 number of points per game. 60 % of these were goals and 40…

Wayne Gretsky scored a Poisson mean 6 number of points per game. 60 % of these were goals and 40 % were assists (each is worth one point). Suppose he is paid a bonus of 3K for a goal and 1K for an assist. (a) Find the mean and standard deviation for the total revenue he earns per game. (b) What is the probability that he has four goals and two assists in one game? (c) Conditional on the fact that he had six points in a game, what is the probability he had 4 in the first half?