**Subject :**Math -3

**Unit :**Statistical Techniques - II

## Constants of Binomial Distribution

**Constants of Binomial Distribution:**

Let the Binomial Distribution be

**Mean,**

μ = E (X) = np

**Standard deviation,**

**First central moment,**

μ = 0

**Second central moment,**

μ_{2} = σ^{2} = npq

**Third central moment,**

μ^{3} = npq (q − p)

**Fourth central moment,**

μ^{4} = 3n^{2} p^{2}q^{2} npq (1 − 6pq)

**Karl Pearson coefficients,**

**Application of Binomial Distribution:**

The use of binomial distribution is made in case of division by dichotomy where one event is called success and another event is called failure. Under certain assumptions and circumstances the nature of binomial distribution is known. It is applicable to the situations of random sampling from finite population with replacement or sampling from an infinite population with or without replacement. The binomial distribution is very useful in decision making situations in business. One area in which it has been very widely applied is quality control. Binomial distribution is considered an important tool in forecasting of the events based on random sampling.