MGF of Poisson

Problem

Moment generating function of a Poisson random variable with rate lam evaluated at t:

M(t) = exp(lam * (e^t - 1)).

Hint

Take E[e^(tX)] and use the Poisson series.

case 1

in: [1,0]

expected: 1

case 2

in: [2,1]

expected: 31.079973004503163

case 3

in: [1,2]

expected: 595.2944153807538

Starter codePython

import math


def mgf_poisson(lam, t):
    # Your code here
    pass

3 test cases · run your code against them in the editor