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Unformatted text preview: 1 ISyE 3044 — Practice Problems for Exam #1 1. Consider the integral D R 1=2 sin . t/dt . (a) Use the following 10 pseudorandom numbers to compute an estimate of . 0.60 0.73 0.35 0.08 0.99 0.47 0.22 0.16 0.54 0.87 (b) Compute an approximate 90% confidence interval for . 2. The random variable X has density function f.x/ D j x j D x if 1 x < 0 x if x 1 . (a) Find the mean E.X/ . (b) Find the c.d.f. F.x/ . 3. Short questions. (a) Suppose that U is a Uniform .0;1/ random variable. What is the distribution of X D 1 5 ln U ? Find the mean of X . (b) The discrete random variable X has the following probability function: k 1 2 3 4 5 P.X D k/ 0.30 0.35 0.20 0.10 0.05 Use the uniform random number U D 0:79 to generate an observation for X . 4. Customers arrive at a post office branch according to a Poisson process with a rate of 2 per minute. (a) What is the expected number of arrivals between 10:30 and 10:40 a.m.? (b) Assume that the post office opens at 9 a.m. with no customers present. What is the proba bility that the third customer will arrive after 9:02 a.m.? (c) Suppose that no customer has arrived between 10 and 10:05 a.m. What is the probability that the next customer will arrive within the next minute? 5. A job shop operates continuously. The interarrival times for jobs are i.i.d. from the following distribution: Interarrival Time (Hours) 1 2 3 Probability .25 .35 .28 .12 2 The processing times are i.i.d. normally distributed with mean 50 minutes and standard deviation 8 minutes. Construct a simulation table, and perform a simulation for 10 customers. Assume that when the simulation begins there is one job being processed (scheduled to be completed in 25 minutes) and there is one job in queue with a 50minute processing time. Use the following uniform .0;1/ observations to generate the interarrival times .53 .37 .08 .62 .53 .56 .14 .67 .82 .68 and the following N.0;1/ numbers to generate the respective processing times 0:23 0:17 0:43 0:02 2:13 0:04 0:18 0:42 0:24 1:17 Round each service time to the nearest integer. In both cases, read from left to right....
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This note was uploaded on 10/23/2011 for the course ISYE 3044 taught by Professor Alexopoulos during the Fall '08 term at Georgia Tech.
 Fall '08
 ALEXOPOULOS

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