Examination Introduction to Stochastic Processes (LNMB/Dutch Master Program) Summary: Examination Introduction to Stochastic Processes (LNMB/Dutch Master Program) Monday December 19, 2005, 12.00 - 15.00 hours This exam consists of 5 problems Use of book is not permitted Motivate your answers! 1. Suppose that print jobs arrive at a network printer with independent and exponentially distributed inter-arrival times with parameter 10 per hour. It takes the printer exactly 6 seconds to print each page. The sizes of the jobs are i.i.d. and have a Poisson distribution with a mean of 2 pages. a. What is the probability that precisely 20 jobs arrive between 8.30 hours and 10.30 hours? b. What is the probability that a print job arrives while the previous job is not finished, when this previous job consists of 6 pages? (Assume that the printing of this previous job started immediately after its arrival). c. What is the expected arrival time of the first job after 12.00 hours, when the previous job arrived at 11.58 hours? d. Let M(t) be the number of print jobs consisting of more than 3 pages that arrive in a time interval (0, t]. Give an expression for P(M(t) = m). 2. In a simple model, the state of a car dynamo at the beginning of year n is Collections: Engineering