”;
${lambda}$ is the shape parameter which indicates the average number of events in the given time interval. The following is the plot of the Poisson probability 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 probability 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 lines of code. What is the probability of exactly 2 errors in 5,000 lines of randomly selected lines of code?
Solution:
The probability of exactly 2 errors in 5,000 lines of randomly selected lines of code is:
”;