Binomial Distribution

Binomial Distribution

This is a special discrete distribution that is premised on the following four conditions:

1. A fixed nuber of trials

2. Each trial is independent

3. The probability of success, ‘p’ is the same for each trial

4. There are only two outcomes: failure or success.

General Formula:

The probability of obtaining n successes out of n independent trials when for each trial the probability of a success p is:

P n =

Notation:

Instead of writing the “Random variable has a binomial distribution.’ There are n independent trials each with a success of p, therefore the following is written:

X ~Bin (n, p)

The quantities n and p are parameters of the distribution, whose values are needed in order to specify the distribution completely.

The mean and variance of this distribution are found by the formulae:

E(X) = n.p

Var (X) = np (1-p)