Hello, I am stuck on all three parts of this question (as shown in the attached picture).

Please help explain, thank you!

1. Let X = (X1, X 2, , X\") be a random sample, where X 1- is a Poisson random variable with mean A > 0. (a) (2 Points) Show the distribution of T = X1 + + Xn is also a Poisson distribution (Hint: please use the MGF method). (b) (3 Points) Show that the sample sum given by T = X1 + + X\" is a sufficient statistic for A (c) (2 Points) Show that the sample sum given by T = X1 + + X\" is a complete statistic for A.(Hint: if ,1 > 0 and 22:0 (111" = 0, then a = 0)