MATH318: Binomial Distribution Facts
A binomial experiment is a probability experiment with
the following properties:
- The experiment consists of n identical trials.
- Each trial has two possible outcomes, which we'll call "success" and "failure".
- The probability of success is the same on every trial.
- 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.