The number of fish that Elise catches in a day is a Poisson random variable with mean

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The number of fish that Elise catches in a day is a Poisson random variable with mean 30.

However, on the average, Elise tosses back two out of every three fish she catches. What is the probability that, on a given day, Elise takes home n fish. What is the mean and variance of

(a) the number of fish she catches,

(b) the number of fish she takes home? (What independence assumptions have you made?)

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