Poisson Distribution Calculator

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Poisson distributioncalculator is very useful tool to find the probability distribution of the given data. This tool uses Poisson distributionrules and formulas. One need to substitute the values only and it helps in finding the result automatically.This can be understood and easily evaluated by the following given below examples:-



Example 1:-

Find the probability of a ball hitting the wall 2 times in 5 mins. If the rate of hitting the ball

according to Poisson processis 2/min.


Solution 1:-

If  N is number of hits received in 1 min.

P(N=2) = e-222/2! = 2e-2

Next is if Q is number of min that had 2 hits in 5 mins. This is a binomial distribution

P(Q=5) = C(5,5)(2e-2)5 ( 1 – 2e-2)5-5

= 32 x e-10 = 0.00145



Example 2:-

Find the probability for r = 1,2,3,4 and 5. The variance of Poisson distribution is 2. This is a

recurrence relation.


Solution 2:-    
                                         

The given variance is 2

P(x=0) = eλ0/0! = e -2 = 0.135

Recurrence relation the formula is

P (x = r+1) = λ/r+1  P(x =r)

P(x=1) = λ/1 P(x=0) = 2 x 0.135 = 0.27

Now substitute all the values 3,4,5 into the formula to get the answer.

P(x=3) = 0.18; P(x=4) = 0.09;  P(x=5) = 0.036







 

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