Question

In a sequence of 8 Bernoulli trials with probability of success p, let X be the number of successes not followed immediately by a failure. Find E(X) (you can use indicators).

Answer 1

Answer:

The value for E(X) is 8p.

Step-by-step explanation:

A Bernoulli trial is a random experiment where there are only 2 outcomes, one with probability p and the other with probability (1-p).

Then, the expected value of a Bernoulli trial Z is p

$E(Z)=p$

If we define X as the sum of 8 random experiments Z, we apply the properties of the expected value to calculate E(X):

$E(X)=E(8\cdot Z)=8\cdot E(Z)=8p$