# Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.42 year. What is the probability that more than five loads occur during a 3 year period?

Jul 19, 2018

The probability is $= 0.7118$

#### Explanation:

The mean time between occurences is $= 0.42 y$

In a $3 y$ period, the number of occurences is

$\lambda = \frac{3}{0.42} = 7.14$

We need more than $5$ loads

Therefore,

The probability is

P(n>5 , 7.14)=1-sum_(n=0)^5(lambda ^n e^(-lambda)/(n!))

=1-(7.14^0 e^(-7.14)/(0!)+7.14^1 e^(-7.14)/(1!)+7.14^2 e^(-7.14)/(2!)+7.14^3 e^(-7.14)/(3!)+7.14^4 e^(-7.14)/(4!)+7.14^5 e^(-7.14)/(5!))

From the tables,

$P \left(n > 5 , 7.14\right) = 1 - \left(0.0008 + 0.0059 + 0.0208 + 0.0492 + 0.0874 + 0.1241\right)$

$= 1 - 0.2882$

$= 0.7118$