# Binomial Distribution

1. The probability that an experiment has a successful outcome is 0.8. The experiment is to be repeated until five successful outcomes have occurred. What is the expected number of repetitions required? What is the variance?

4. In a lot of 10 components, 2 are sampled at random for inspection. Assume that in fact exactly 2 of the 10 components in the lot are defective. Let X be the number of sampled components that are defective.

a. Find P(X=0).

b. Find P(X=1).

c. Find P(X=2).

d. Find the probability mass function of X.

e. Find the mean of X.

f. Find the standard deviation of X.

https://brainmass.com/statistics/probability/probability-experiment-successful-outcome-171179

#### Solution Preview

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1. The probability that an experiment has a successful outcome is 0.8. The experiment is to be repeated until five successful outcomes have occurred. What is the expected number of repetitions required? What is the variance?

Let X denotes the number of repetitions of the experiment required to get five successful outcomes. Then X can take values 5, 6, 7, ....

Now the probability mass function (p.m.f) of X is given by,

P[X=x] = P[ The number of repetitions required to get 5 successful outcome is x]

= P[There are 4 successful ...

#### Solution Summary

The solution contains the identification of the probability distribution for a specified problem and the determination of mean, variance and p.m.f of the distribution.