Arena Simulation and Pseudo-Random Number Generators, Exams of Nursing

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QUESTIONS AND ANSWERS

EXAM

ISYE6644 Simulation Midterm 2 -

Exam

TESTED AND CONFIRMED A+ ANSWERS

What is the name of Arena's primary modeling approach "world view"? A) Process-Interaction B) Event-Scheduling C) Continuous Modeling Flowchart D) Mixed Modeling E) Event-Interaction - ANSWER-A) Process Interaction What sequence of Arena modules would you use to generate customer arrivals, use a server , and then have customers leave the system after they're done with the server? - ANSWER-Create-Process-Dispose (ARENA) TRUE or FALSE? A Create module allows you the use a variety of customer interarrival time distributions. - ANSWER-TRUE (ARENA) What is Seize-Delay-Release? - ANSWER-Grab at least one resource (server), spend time getting served, and then free the server for the next customer. If you seize and the server isn't available, you may have to wait in a queue. (ARENA) What is a seize-delay? - ANSWER-Grab at least one resource and spend time getting served. Remember to release the server sometime later, else he gets deadlocked and a giant line will form. (ARENA) What is a delay-release? - ANSWER-Use a previously seize'd for a while, and then free him for the next guy to use. (ARENA) Which of the following action sequences can you find in a Process module? A) Delay B) Seize-Delay C) Delay-Release D) Seize-Delay-Release E) All of the above - ANSWER-all of duh abuv (ARENA) TRUE or FALSE? A process is generally considered to consist of both a resource and its associated queue. - ANSWER-TRUE (ARENA) TRUE or FALSE? You can change the number of servers on duty (i.e., the capacity) for a resource using the Resource spreadsheet. - ANSWER-TRUE

What can go wrong with LCGs? - ANSWER-Something like Xi = (4Xi- 1 + 2)mod8 is not full period, since it only produces even integers Something like Xi = (Xi- 1 +1)mod8 is full period, but it produces very non-random output X1 = 1, X2 = 2, etc. In any case, if m is small, you'll get quick cycling whether or not the generator is full period. And just because m is big, you still have to be careful (RANDU generator) What is an XOR function? - ANSWER-BI = (BI-r + BI-q) mod 2 TRUE or FALSE? RANDU is a pretty good generator. - ANSWER-False TRUE or FALSE? There are good PRN generators out there having incredible cycle lengths of over 2100. - ANSWER-True TRUE or FALSE? (1 XOR 1) XOR 1 = 1. - ANSWER-True What are the two different types of tests for random number generators? - ANSWER- Goodness-of-fit tests - are the PRNs approximately Unif(0,1) Independence tests - are the PRNs approximately independent? Type 1 error is when you reject the null hypothesis even though it is true. T/F - ANSWER-True Type 2 error is when you accept the null hypothesis even though it is false. T/F - ANSWER-True TRUE or FALSE? =(𝑅𝑒𝑗𝑒𝑐𝑡0|0𝑖 𝑡𝑟𝑢𝑒) is the probability of a Type I error. - ANSWER-True In the context of evaluating a PRN generator, which kinds of statistical tests are we interested in? (a) Goodness-of-fit tests (b) Independence tests. (c) Neither (a) nor (b). (d) Both (a) and (b). - ANSWER-(d) Both (a) and (b). If the 2 goodness-of-fit statistic, 20, is much greater than the relevant quantile 2,−1, what do we do? a) Reject the goodness-of-fit test and declare that the PRNs are probably not uniform. b) Reject the goodness-of-fit test and declare that the PRNs are probably not independent.

c) Accept the goodness-of-fit test and declare that the PRNs are probably uniform. d) Accept the goodness-of-fit test and declare that the PRNs are probably independent. e) Panic at the disco! - ANSWER-a) Reject the goodness-of-fit test and declare that the PRNs are probably not uniform. What is a run? - ANSWER-A run is a series of similar observations. What is a run test? - ANSWER-A runs test will reject the null hypothesis of independence if there are too many or too few runs, whatever that means. TRUE or FALSE? Unif(0,1) pseudo-random numbers can be used to generate pretty much any other random variates, e.g., exponential, normal, and Poisson. - ANSWER- True If is a continuous random variable with c.d.f. (), what's the distribution of ()? Unif(0,1) Nor(0,1) Triangular Exp() All of the above - ANSWER-Unif(0,1) If is a Unif(0,1) random variable, what's the distribution of − 1 𝑙(1−)? Unif(0,1) Nor(0,1) Triangular Exp() All of the above - ANSWER-Exp() TRUE or FALSE? If you can't find a good theoretical distribution to model a certain random variable, you might want to use the empirical distribution of the data to do so. - ANSWER-True TRUE or FALSE? The convolution method involves sums of random variables. - ANSWER-True Suppose that 1 and 2 are PRNs. What's the distribution of 1+2? Unif(0,2) Nor(0,2) Triangular(0,1,2) Exp(1/2) Exp(2) - ANSWER-Triangular(0,1,2)