# Again answer questions a b and c 212 a ashlight

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ing. Let T1 , T2 , T3 , . . . be the arrival times of a Poisson process with rate , and let U1 , U2 , . . . Un be independent and uniformly distributed on [0, t]. If we condition on N (t) = n, then the set {T1 , T2 , . . . Tn } has the same distribution as {U1 , U2 , . . . , Un }. 2.6 Exercises Exponential distribution 2.1. Suppose that the time to repair a machine is exponentially distributed random variable with mean 2. (a) What is the probability the repair takes more than 2 hours. (b) What is the probability that the repair takes more than 5 hours given that it takes more than 3 hours. 2.2. The lifetime of a radio is exponentially distributed with mean 5 years. If Ted buys a 7 year-old radio, what is the probability it will be working 3 years later? 2.3. A doctor has appointments at 9 and 9:30. The amount of time each appointment lasts is exponential with mean 30. What is the expected amount of time after 9:30 until the second patient has completed his appointment? 2.4. Copy machine 1 is in use now. Machine 2 will be turned on...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online