Binomial Random Variables

Binomial Random variables help us to make a link between probability and numbers that we observe as data.

Binomial Random Variable: A numerical valued function defined on a sample space. A random variable X “maps” an outcome in a sample space to a numerical value. We use capital letters such as X or Y to denote binomial random variables. Let s be an elementary outcome. A value, X(s), of X is denoted x.

A binomial random variable is discrete if it can take on a finite or countable number of values. A continuous random variable takes on an uncountable number of values.
Binomial Random Variable:

General features of a Binomial Random Variable:

* The binomial random experiment consists of n identical trials.
* Possible outcomes on each trial are of only two. given one outcome by S (for Success) and the other by F (for Failure).

* The probability for Success(S) remains the same from trial to trial. Denote it by p=Pr(Success).

* The trials of binomial random experiment are independent of each other.

* Then we say Binomial Random Variable X as the number of Successes in n trials.