Sum of independent poisson random variables

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n this problem we show directly that the sum of independent Poisson random variables is Poisson. Let J and K be independent Poisson random variables with expected values α and β respectively, and show that N = J + K is a Poisson random variable with expected value α + β.

And then simplify the summation by extracting the sum of a binomial PMF over all possible values.

Reference no: EM131084112

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