# Binomial Distribution

This is a discrete distribution

A discrete random variable is said to follow a binomial distribution with parameters n and p, written X~B(n,p)

if its probability distribution satisfies the following equation

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### Properties

Expected Value E(x) = np

Variance V9x) = np(1-p)

### Assumptions

1) There can only be two possible results in each time or space interval

2) The total number of trials is fixed in advance

3) The outcomes are independent

4) All the trials have the same probability of success.

### Example

The good example of a binomial distribution would be the tossing of a coin.

What is the probability of getting 3 heads in 10 tosses (x=3 and n=10)

Plot graph of B(10,0.5)

The parameter p is the proportion of the population taking the "success" outcome

It can also be applied to product failures, for example what is the probability of producing x defective items in a batch of n.

### Excel Functions

__BINOM.DIST__ - (2010 - BINOMDIST) The probability of getting less than or equal to a particular value in a binomial distribution.__BINOM.INV__ - (2010 - CRITBINOM) The smallest number of successes required to get greater than a particular value in a binomial distribution.

This is concerned with 2 items

This is a distribution that has 2 humps

BINOMDIST(num successes, num trials, prob of success, cumulative) - if cumulative is set to zero, gives probability of the number of successes out of the number of trials assuming the probability of each success is "prob of success".

If cumulative is any other value then it gives probability of 0,1,2, to num of successes ??

### Negative Binomial Distribution

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