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[See Steps] Let N, X 1 , X 2 ,… be independent random variables where N has a Poisson distribution with mean 5 while X1, X2,… each has a Poisson distribution

Question: Let N, X 1 , X 2 ,… be independent random variables where N has a Poisson distribution with mean 5 while X1, X2,… each has a Poisson distribution with mean 2.

  1. Determine E [ N \[\sum\limits_{i=1}^{N}{{{X}_{i}}}\] ]
  2. Determine the variance of \[\sum\limits_{i=1}^{N}{{{X}_{i}}}\]

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