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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).

Respuesta :

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

[tex]E(Z)=p[/tex]

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

[tex]E(X)=E(8\cdot Z)=8\cdot E(Z)=8p[/tex]

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