The number of calls to a roadside assistance company has an approximate Poisson distribution with an average of one call every two hours

Question

The number of calls to a roadside assistance company has an approximate Poisson distribution with an average of one call every two hours.

1) Give the probability mass function of N= the number of calls received in 4 hours.

2) Give the probability density function of W= the time until the first call is received.

3) Show how the distribution of W can be used to find the probability that the time until the first call is more than 4 hours. (Full credit for setting up the integral with the correct integrand and limits of integration. You do not need to integrate.)

4) Use the distribution of N to find the probability that the time until the first call is more than 4 hours.

5) Give the probability density function for T= the time until the third call is received.

Answer 1

1/2 call every hour...

Prob( X=k) = (1/2)^k / (k! * e^(1/2))

I posted the distribution table for you in a spreadsheet called Poisson Phone.xls

in the resource section under Toolkit menu