a) Find the mean, variance, and moment generating function of N(t), as given by (2.17). b) Show by discrete convolution that the sum of two independent Poisson rv’s is again Poisson. c) Show by using...

a) Find the mean, variance, and moment generating function of N(t), as given by (2.17).

b) Show by discrete convolution that the sum of two independent Poisson rv’s is again Poisson.

c) Show by using the properties of the Poisson process that the sum of two independent Poisson rv’s must be Poisson.