The number of goals that J scores in soccer games that her team wins is Poisson with

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The number of goals that J scores in soccer games that her team wins is Poisson with mean 2, while the number she scores in games that her team loses is Poisson with mean 1. Assume that J’s team wins each game they play with probability p.

(a) Find the expected number of goals that J scores in her next 3 games.

(b) Find the probability that she scores a total of n goals in her next 3 games.

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