Basis

Binomial Distribution

Poison Distribution

Definition

Binomial distribution is defined as one of the types of probability distribution in which the probability of repeated number of trials is studied.

Poisson Distribution is defined as one of the types of probability distribution which gives the count of independent events occurs randomly with a given period of time.

Nature

It is Biparametric in nature which indicates that it is featured by two parameters ‘n’ and ‘p’.

It is Uniparametric in nature which indicates that it is featured by only one parameter ‘m’.

Outcomes

In the case of the binomial distribution, there are only two possible outcomes (success or failure).

In the case of poison distribution, there are unlimited numbers of possible outcomes.

Mean and Variance

In the case of the binomial distribution, Mean is greater than Variance.

In the case of poison distribution, Mean is equal to Variance.

Business

Applications

Binomial Distribution can be used by Banks and other financial institutions to determine the likelihood of borrowers defaulting and figuring out how much money to keep in reserve, or how much to loan.

Poison Distribution can be used by service industries to predict customer sales on particular days of the year as well as can be useful in estimating demand and supply.

Example

Tossing a Coin (Outcomes: Head or Tail)

A number of people using an ATM located outside the XYZ office.(Outcomes: Unlimited)

Formula

P (X) = ⁿC_x p^x q^n-x

P(X) = µ^x e^{– µ}/x!