Question

You are given that claims are reported according to a homogeneous Poisson process. Starting from time zero, the expected waiting time until the second claim is three hours. Calculate the standard deviation of the waiting time until the second claim.

Answer 1

Answer:

1.732

Step-by-step explanation:

You are given that claims are reported according to a homogeneous Poisson process

LetX be the waiting time from 0 to second claim

X is Poisson with averageof 3 hours.

We know in a Poisson distribution the mean = variance

Hence average waiting time = mean = 3

This will also be equal to var(x)

Var(x) = mean of Poisson distribution= 3

Hence standard deviation = square root of variance

=$\sqrt{3} \\=1.732$