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# Characteristic Function

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Let X1 and X2 be two jointly distributed, statistically independent Poisson random variables, where E[X1]=&#955;1 and E[X2]=&#955;2 . Using a random variable defined by N= X1 + X2

What is the characteristic function of X1? What is the pmf of N? What is the variance of N in terms of &#955;1 and &#955;2?

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The solution describes the determination of the characteristic function and pmf of a random variable.

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Let X1 and X2 be two jointly distributed, statistically independent Poisson random variables, where E[X1]=λ1 and E[X2]=λ2 . Using a random variable defined by N= X1 + X2. What is the characteristic function of X1? What is the pmf of N? What is the variance ...

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