Solved: Patients arrive at a hospital emergency department

Solution

Step 1 of 2

a) We have to find the mean time until 10th  arrival

Given that the patients arrive at a hospital with a poisson process with mean of 6.5 per hour

Then

Let X be the time until the 10th  arrival

Here X is following the gamma distribution

Here

The mean of gamma distribution is

The Mean (

                        =

                        =10/6.5

                        =1.538

Hence the mean time until 10th  arrival is 1.538