Let X1, X2, . . . be a sequence of independent and identicallydistributed random variables where the distribution is given by theso-called zero-truncated Poisson distribution with probability massfunction; P(X = x) = λx/ (x!(eλ − 1)), x = 1, 2,3...
Let N ∼ Binomial(n, 1−e^−λ ) be another random variable that isindependent of the Xi ’s.
1) Show that Y = X1+X2 + ... + XN has a Poisson distributionwith mean nλ.
