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Mean of Poisson Random Variable

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Let X and Y be two jointly distributed random variables with joint characteristic function

Where α, β, and γ are positive constants. Y is a Poisson random variable with what mean?

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The mean of Poisson random variables are examined.

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The statement of the problem is lacking in that it does not say which of the two omegas relates to Y.

In the attached explanations, I assumed that it is ω_2.

Let X and Y be two jointly distributed random variables with joint ...

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