Poisson Distribution Variance Help

Introduction to Poisson Distribution Variance Help:

In Poisson distribution, x is called as discrete random variable. Lambda is called as the Poisson distribution parameter in a Poisson experiment. In affixed period of time interval, the number of events is occurred when the events happened in random with separate time and constant rate. While lambda is huge, the Poisson distribution is related to the standard normal distribution with lambda be the occurrence rate of proceedings per unit time. Let us see about Poisson distribution variance help in this article.

General Formula for Poisson Distribution Variance Help:
Formula for Poisson distribution problem is:

Formula:

`Poisson distribution =` `(e^(-lambda) lambda^(x))/(x!)`

Where,

x means Poisson value
`lambda` means rate of change
e means log funct ion


Variance of Poisson Distribution:

In poisson distribution, `lambda` represents the variance of Poisson distribution.

Variance Formula

`V(X) = sigma^(2) = lambda`

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Worked Examples to Poisson Distribution Variance Help:
Example 1 for Poisson Distribution Variance Help

Solving the variance of Poisson distribution if `P(X = 2) = P(X = 3)` and also find `P(X = 6)`

Solution

Given `P(X = 2) = P(X = 3)`

Therefore, we have `(e^-lambda lambda^2)/(2!)` = `(e^-lambda lambda^3)/(3!)`

`=>`  `3 lambda^(2) = lambda^(3)`

`=>`  `lambda^(2) (3 - lambda) = 0 `  as `lambda!= 0` .

Variance of the Poisson distribution is `lambda = 3`

`P(X = 6) =` `(e^-lambda lambda^6)/(6!)`

` = (e^-3 (3)^6)/(6!)`

` = ((0.049787)(729))/(720)`

`= (36.2947)/(720)`

`P(X = 6) = 0.05040`

Therefore, the variance of poisson distribution for above given values are 0.05040.

Example 2 for Poisson Distribution Variance Help

Solving the variance of poisson distribution if `P(X = 3) = P(X = 4)` and also find `P(X = 9)`.

Solution

Given `P(X = 3) = P(X = 4)`

Therefore, we have `(e^-lambda lambda^3)/(3!)` = `(e^-lambda lambda^4)/(4!)`

`=>`  `4 lambda^(3) = lambda^(4)`

`=>`  `lambda^(3) (4 - lambda) = 0 `  as `lambda!= 0` .

Variance of the poisson distribution is `lambda = 4`
`P(X = 9) =` `(e^-lambda lambda^9)/(9!)`

` = (e^-4 (4)^9)/(9!)`

`= ((0.01831)(262144))/(362880)`

`= (4799.8566)/(362880)`

`= 0.01323`

Therefore, the variance of poisson distribution for above given data is 0.01323.