## 13.6 Outline

- Random variables
- definition
- binomial random variable
- binomial distribution

- Binomial experiments
- definition; four conditions
- fixed number of trials
- two mutually exclusive outcomes
- trials are independent
- probabilities remain constant for each trial

- binomial distribution theorem
- Bernoulli trials

- definition; four conditions

## 13.6 Essential Ideas

**Binomial Experiment**

A **binomial experiment** is an experiment that meets four conditions.

- There must be a fixed number of trials; denote this by
*n*. - There must be two possible mutually exclusive outcomes for each trial. Call them
*success*and*failure*. - Each trial must be independent.
- The probability of success and failure must remain constant for each trial.

**Binomial Distribution Theorem**

Let *X* be a random variable for the number of success in *n *independent and identical repetitions of an experiment with two possible outcomes, success and failure. If *p* is the probability of success, then for *k* = 0, 1, … , *n*,