Use theorem to obtain the characteristic function of a

Question

1. Use Theorem to obtain the characteristic function of a normal random variable with mean µ and variance σ² from that of a standard normal random variable.

2. Use characteristic functions to show that if X₁ and X₂ are independent Poisson random variables with parameters λ₁ and λ₂, then X = X₁ + X₂ is Poisson with parameter λ= λ₁ λ₂. Generalize this to the sum of n Poisson random variables.