Electrical Engineering > Final Exam Review > ESE 503 - University of Pennsylvania _ ESE503 - Simulation Modeling & Analysis (Final Exam) Spring S (All)
ESE503 - Simulation Modeling & Analysis (Final Exam) Spring Semester, 2021 M. Carchidi Problem #1 (25 points) - Chapter 8 Suppose that X is a mixed random variable having pdf/pmf fx ... Ae3x, when − x 0 A, when x 0 Ae−6x, when 0 x . a.) (5 points) Determine the value of A. b.) (15 points) Determine how a single sample of X can be constructed from a single random number R U0,1. b.) (5 points) Determine the numerical values of EX and VX. Hint: You may use the fact that − 0 xneaxdx −1nn! an1 and 0 xne−axdx ann!1 for n 0,1,2,... and a 0. Problem #2 (15 points) - A Non-Stationary Poisson Process Consider a non-stationary Poisson process having time-dependent rate function t 12t, when 0 hours t 2 hours 24, when 2 hours t 5 hours 64 − 8t, when 5 hours t 8 hours in units of customers per hour, over an 8-hour day from 9:00 AM - 5:00 PM. Compute the probability that more that 111 customers arrive into the store between the hours of 10:00 AM and 3:00 PM. Problem #3 (20 points) - Chapter 8 a.) (12 points) Consider a continuous random variable X having pdf fx 2 Γ1/4 e− 14 x4 for − x . Develop an acceptance-rejection algorithm for sampling X using the symmetric two-sided exponential distribution with pdf gy 1 2 e−|y| for − y , as a basis. b.) (8 points) Using the fact that Γ1/4 ≃ 3.6256, compute the probability that your algorithm in part (a) will require fewer than three (3) iterations to produce a sample of X. Problem #4 (20 points) - Chapter 6 Suppose that customers enter a store so that the interarrival time between customers is exponential with a mean of 0.8 minutes per customer. In the store, there are c identical servers all working in parallel and all with a common service-time distribution that is geometric, ps 1 − ps−1p for s 1,2,3,..., in minutes, with a mean service time of 3 minutes per customer. a.) (5 points) Determine the smallest value of c so that steady-state conditions will exist for this queueing system. b.) (15 points) Using your value of c determined in part (a), compute the steady-state values of: , LQ, wQ, w and L, each worth 3 points. ——————————————————————————————————————— Problem #5 (20 points) - Chapter 9 Consider a random variable X with pdf fx, 1 2 3x−1lnx2 for 0 x 1 and 1 . If an n-point sample of X Sn X1,X2,X3,… ,Xn, is taken, a.) (10 points) determine an expression for the maximum-likelihood estimator of (ML) in terms of 〈lnX 1 n ∑ k1 n lnXk. b.) (5 points) Given also that xnlnx2dx xn1 n 12lnx n2 − 21n3 1lnx 2 for n 0, and lim x→0 xn lnx 0 and lim x→0 xnlnx2 0 for n 0, determine an expression for the sample-mean estimator of (SM) in terms of 〈X 1 n ∑ k1 n Xk. c.) (5 points) Given the 5-point data sample S5 0.2,0.8,0.3,0.4,0.1, compute the numerical values of ML and SM. [Show More]
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