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## What is the Binomial Distribution?

It is a probability distribution for a random variable that can take on only two distinct values. For example, we take a random variable X with respect to a coin. X has only two discrete possibilities - Heads or Tails. The observation ‘head or tail’ is recorded for each toss.

## The Binomial Distribution Criteria

• The number of observations n will be fixed.
• Each and every observation is independent.
• Each observation only two outcomes
• The probability of success is the same from one trial to another.

The formula of Binomial Distribution is

b(x; n, P) = nCx * Px * (1 – P)n – x

Where

x = total number of “successes”.

n = number of trials.

P = probability of success on an individual trial.

b = binomial probability

## The Use Of Biomial Distribution

The binomial distribution is generally used to define the probability. You can determine the success yield of your company with the use of n & p parameters. The binomial distribution is the main part of statistics which will be helpful to determine some calculations. It is used to model the probability of obtaining one of two outcomes, a certain number of times (x), out of a fixed number of trials (n) of a discrete random event.

## Properties of Binomial Distribution

The Students who would like to learn binomial distribution should be aware of the properties of the binomial distribution. The binomial distribution has three primary attributes. They are the arithmetic mean, standard deviation and pattern or shape of the distribution.

• The mean of the binomial distribution is μ = nP
• The value of binomial distribution depends on two parameters & it may be uni-modal or bi-modal.
• The standard deviation of the binomial random variable measures the dispersion of the binomial distribution. The standard deviation is determined by σ² = npq

## Topics by our Binomial Distribution Assignment Help experts

 Bernoulli distribution Conditional binomials Sum of binomials Poisson binomial distribution Limiting distributions Normal approximation Poisson approximation Beta distribution Poisson approximation

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