Statistics Tutorial
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Cumulative Poisson Distribution
Statistics - Cumulative Poisson Distribution
${lambda}$ is the shape parameter which indicates the average number of events in the given time interval. The following is the plot of the Poisson probabipty density function for four values of ${lambda}$. Cumulative Distribution Function.
Formula
$${F(x,lambda) = sum_{k=0}^x frac{e^{- lambda} lambda ^x}{k!}}$$
Where −
${e}$ = The base of the natural logarithm equal to 2.71828
${k}$ = The number of occurrences of an event; the probabipty of which is given by the function.
${k!}$ = The factorial of k
${lambda}$ = A positive real number, equal to the expected number of occurrences during the given interval
Example
Problem Statement:
A complex software system averages 7 errors per 5,000 pnes of code. What is the probabipty of exactly 2 errors in 5,000 pnes of randomly selected pnes of code?
Solution:
The probabipty of exactly 2 errors in 5,000 pnes of randomly selected pnes of code is:
${ p(2,7) = frac{e^{-7} 7^2}{2!} = 0.022}$ Advertisements