Jobs are sent to a printer at an average rate of 3 jobs per

Jobs are sent to a printer at an average rate of 3 jobs per hour.

1) What is the probability of observing a time between jobs of more than 1 hour?

2) What is the probability that the next job is sent within 5 minutes?

3) What is the probability of observing a time between jobs between 10 and 15 minutes?

4) What is the exp0ected time between jobs?

5) What is the median time between jobs?

Solution

4)

expected time between jobs = 1/lambda = 1/3 = 20 minutes

2)

P(X < 1/12) = 1 -e^(-3/12) = 0.2212

1)

observing time between jobs of more than 1 hour

P(X >1) = e^(-3) = 0.0498

3)

P(10 < X < 15) = P(X<15) - P(X <10)

= 1 -e^(-3/4) - 1 + e^(-1/6)

= 0.709

5)

medain = ln(2)/lambda = 13.86 minutes