Answer to Question #340157 in Statistics and Probability for Maneo

Question

1. Let X be a random variable having a Bernoulli distribution. Then

• a) E[X] = p

• b) V[X] = pq = p(1-p)

• c) M_X(t) = pe^t + q

• Prove the above equalities.

2.Let 𝑋 be a Bernoulli probability mass function with

M_X(t) = pe^t + q

Derive the mean and variance of 𝑋.

Answer 1

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