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)

Var (Y) = 15/4

Step-by-step 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.