Solve Using Poisson Distribution

Poisson distribution becomes the major part in the statistical maths and their aim is to render the average of the given functions. In the Poisson distribution, we will find out the rate of change of function for the given function. This can be made possible by finding two values namely , x value means the event in success and lambda value means the change in average functions. In this article we will illustrate about solving Poisson distribution.

Poisson distribution model is defined as the important chapter in mathematics. The main function of the model of Poisson distribution is to find the average of the given distribution functions. For this model, we are using the formula given for Poisson distribution. The value of x given in the formula is mainly used for the success events. And the value of lambda given in the formula is mainly used for defining the rate of change.

Poisson distribution in statistics are defined as one of the most important chapter. For solving the Poisson distribution we are having one of the formula. By using the formula given for the Poisson Distribution we are calculating the average values. According to the rate of change function we have to calculate the Poisson distribution average.

Explanation to the Solve Use Poisson Distribution:

In the statistics, Poisson distribution is used to calculate the rate of change of function.Here we can learn and solve the Poisson distribution problems.Here we will brief about the solve use Poisson distribution using examples.

The formula for the Poisson distribution is given as follows,

Formula:

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

where,

x = Poisson value
lambda = Rate of change
e = Log function
Example Problems to Solve Use Poisson Distribution:

Example 1- Solve use Poisson distribution

Solve Poisson distribution where,lambda = 7 x = 13 and e = 2.718

Solution:

Step 1: Given:

lambda = 7

x = 13

Step 2: Formula:

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

Step 3: To find e:

e-7 = (2.718)-7

= 0.0009118

Step 4: Solve:

lambda =7

x = 13

lambda^x = (7)13 = 96889010407

Step 4: Substitute:

((e^-lambda)(lambda^x))/(x!) = (0.0009118(96889010407))/(13!)

= 88343399.6891026/(6227020800)

= 0.014

Result: Poisson Distribution = 0.014

Example 2- Solve use Poisson distribution

Solve Poisson distribution where,lambda = 8, x =11 and e = 2.718

Solution:

Step 1: Given:

lambda = 8

x = 11

Step 2: Formula:

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

Step 3: To find e:

e-8 = (2.718)-8

= 0.0003354

Step 4: Solve:

lambda =8

x = 11

lambda^x = (8)11 = 8589934592

Step 4: Substitute:

((e^-lambda)(lambda^x))/(x!) = (0.0003354(8589934592))/(11!)

= 2881064.0621568/(39916800)

= 0.072

Result: Poisson Distribution = 0.072

Practice Problems to the Solve Use Poisson Distribution:

Example 1- Solve use Poisson distribution

Solve Poisson distribution where,lambda = 22, x = 24and e = 2.718

Answer: 0.074

Example 2- Solve use Poisson distribution

Solve Poisson distribution where,lambda = 19, x =20 and e = 2.718

Answer: 0.087