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Please answer in detail so that i can understand. The number of goals that J scores...

Please answer in detail so that i can understand.

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 team’s next game. Suppose J’s team has just entered a tournament in which they will continue to play games until they lose. Let X be the total number of goals scored by J in the tournament.

(b) Find E[X].

(c) Find P(X = 0).

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