5. Problem 6.5.8 In 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 a and , respectively. Show that NJ+K is a Poisson random variable with expected value a+. Hint: Show that n - Py (n) P (m)P, (n-m) 702-0 and then simplify the summation be extracting the binomial PMF over all possible values. sum of a