MediumProbabilitypr-040

MGF of Bernoulli

Problem

Moment generating function of a Bernoulli(p) random variable evaluated at t.

M(t) = (1 - p) + p * e^t.

Hint

Take the expectation of e^(tX) over X in {0, 1}.

case 1

in: [0.5,0]

expected: 1

case 2

in: [0.5,1]

expected: 1.8591409142295225

case 3

in: [0.2,2]

expected: 2.2778112197861304

case 4

in: [0,3]

expected: 1

Starter codePython

import math


def mgf_bernoulli(p, t):
    # Your code here
    pass

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