Today, I would like to extend my previous topic on discrete probability distribution with the concept of Binomial Distribution.

A binomial distribution is a specific probability distribution. It is used to model the probability of obtaining one of two outcomes, a certain number of times k out of fixed number of trials N of a discrete random event. A binomial distribution has only two outcomes: the expected outcome is called a success and any other outcome is a failure. The probability of a successful outcome is P and the probability of a failure is 1 – P.

The below rules must be followed:

Rule #1: There are only two mutuallyexclusive outcomes for a discrete random variable (i.e. success or failure).

Rule #2: There is a fixed number of repeated trials (i.e., successive tests with no outcome excluded).

Rule #3: Each trial is an independentevent (meaning the result of one trial doesn’t affect the results of subsequent trials).

Rule #4: The probability of success for each trial is fixed (i.e., the probability of obtaining a successful outcome is the same for all trials).

Real life use of Binomial Distribution:

Product quality control test.

Product buy frequency test.

Employee performance factor analysis.

Formula of Binomial Distribution to calculate mean and standard deviation:

The mean of a binomial distribution with parameters N (the number of trials) and π (the probability of success on each trial) is:

μ = Nπ

where μ is the mean of the binomial distribution. The variance of the binomial distribution is:

σ^{2} = Nπ(1-π)

where σ^{2} is the variance of the binomial distribution.

Probabilities for a binomial random variable X can be found using the following formula for p(x):

In general, to calculate “n choose x,” one may use the following formula: