Question

A Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.60 year.
(c) How long must a time period be so that the probability of no loads occurring during that period is at most 0.13?

Answer 1

Since it is a Poisson process, we can safely use the Poisson distribution to model the problem.
Given \(\lambda=0.6 \)= mean time between occurrences, and the Poisson distribution (pdf) is given by:
P(X=k)=\(\dfrac{e^{-\lambda}\lambda^k}{k!}\)
We set k=0 (no occurrence)
and P(X=0)=0.13 to solve for lambda.
0.13=\(\dfrac{e^{-\lambda}\lambda^0}{0!}=e^{-\lambda}\)
Solving gives \(\lambda=2.04\)
which means the time period would have an average of 2.04 occurrences, or
time = 2.04*0.6 = 1.224 years.

Answer 2

thanks a buch!!

Answer 3

You're welcome! :)