Poisson process can be used to represent the occurrence of

Lennie Davis

Lennie Davis

Answered question

2022-01-16

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?

Answer & Explanation

Paineow

Paineow

Beginner2022-01-16Added 30 answers

The probability is =0.7118
Explanation:
The mean time between occurences is =0.42y
In a 3y period, the number of occurences is
λ=30.42=7.14
We need more than 5 loads
Therefore,
The probability is
P(n>5,7.14)=1n=05(λneλn!)
=1(7.140e7.140!+7.141e7.141!+7.142e7.142!+7.143e7.143!+7.144e7.144!+7.145e7.145!)
From the tables,
P(n>5,7.14)=1-(0.0008+0.0059+0.0208+0.0492+0.0874+0.1241)
=1-0.2882
=0.7118

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