Poisson Distribution Example
This worksheet may help you to know about the Poisson Distribution. Poisson Distribution is a continuous probability function which takes average rate of success and Poisson random variable as inputs and gives the output values of Poisson Distribution. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume. The formula used to calculate Poisson Distribution is,
Poisson Distribution Formula
Where e is the base of the natural logarithm equal to 2.71828..
K is the number of occurrences of an event; the probability of which is given by the function
k! is the factorial of k
λ is a positive real number.
Poisson Distribution Examples
1. Calculate the Poisson Distribution whose λ (Average Rate of Success)) is 3 & X (Poisson Random Variable) is 6.
Substitute these values in the above formula,
f = 36 x e-3/6!
= 729 x 0.0498 / 720
2. A manufacturer of television set known that on an average 5% of their product is defective. They sells television sets in consignment of 100 and guarantees that not more than 2 set will be defective. What is the probability that the TV set will fail to meet the guaranteed quality? e-5 = 0.0067
Success = the TV is defective
X = number of successes
p = probability of success = 5% = 0.05
n = 100 , λ = np = 100 x 0.05 = 5
Poisson Distribution is
P(X=x) = e-λ λx /x! ; x=0,1,2,3,4
Guarantee: X not less than 2 => X= 0,1,2
P(X > 2) = 1- [P(0)+ P(1) + P(2)]
= 1 - e-5 [1 + 5 + 25/2 ]
= 1 - e-5 (37/2)
= 1 - (0.0067) x 37/2
= 1 - 0.12395
The above worksheet will help you to understand how to calculate Poisson Distribution when it comes to online calculation this Poisson Distribution Calculator is an essential tool to make the calculation easy.
Poisson Distribution Practice Problems