Let N1 and N2 be independent random variables following

Chapter , Problem 44

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Let \(N_1\) and \(N_2\) be independent random variables following Poisson distributions with parameters \(\lambda_1\) and \(\lambda_2\). Show that the distribution of \(N = N_1+ N_2\) is Poisson with parameter \(\lambda_1+\lambda_2\).

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