MATH318: Binomial Distribution Facts

A binomial experiment is a probability experiment with the following properties:
  1. The experiment consists of n identical trials.
  2. Each trial has two possible outcomes, which we'll call "success" and "failure".
  3. The probability of success is the same on every trial.
  4. The trials are independent events; the outcome of each trial is not affected by the outcomes of the other trials.

Let x be the number of successes in a binomial experiment. Then x is a discrete random variable. The probability distribution associated with x is called a binomial probability distribution.

The value of this probability distribution function is given by:

P(x=a) = f(a) = pa * (1-p)n-a * (n!) / ((n-a)! * (a!))

The factorial function is defined as the product:

m! = m * (m-1) * (m-2) . . . 3 * 2 * 1.