Question

Let X be the number of independent Bernoulli trials performed until a success occurs.

Let Y be the number of independent Bernoulli trials performed until 5 successes occur.

A success occurs with probability p and Var(X) = 3/4

Calculate Var(Y)

Answer 1

Var(Y) = 15/4

Explanation:

Y is basically 5X, since X is the number of trials until a success happens, and Y is the number of trials until 5 successes happens.

We have that

Var(X) = 3/4

So

Var(Y) = Var(5X) = 5*Var(X) = 5*(3/4) = 15/4.