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ISYE6644 SIMULATION MIDTERM TEST FINAL
If ๐ is a continuous random variable with c.d.f. ๐น(๐ฅ), what's the distribution of ๐น(๐)? Unif(0,1) Nor(0,1) Triangular Exp(๐) All of the above - Unif(0,1) If ๐ is a Unif(0,1) random variable, what's the distribution of โ1๐๐๐(1โ๐)? Unif(0,1) Nor(0,1) Triangular Exp(๐) All of the above - Exp(๐) 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 - 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? - Create-Process-Dispose (ARENA) TRUE or FALSE? A Create module allows you the use a variety of customer interarrival time distributions. - TRUE (ARENA) What is Seize-Delay-Release? - 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? - 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? - 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?
What is a random device? - Considered a lousy generator, nice randomness properties. However, Unif(0,1) sequence storage is tough so it's tough to repeat experiment. An example is flip a coin or least significant digits of atomic clock What is a random number table? - It is a lousy random number generator that used to be used in like the 1950s, lots of digits supplied in tables. What is the mid-square method (J. von Neumann) for random number generation? - Idea: Take the middle part of the square of the previous random number. Its pretty shitty and it tends to degenerate (all results end up being 0 at some point when you are iterating) Which of the following PRN generators aren't very good? a) Generators involving physical devices such as coin flips or least significant digit readings from an atomic clock. b) Random number tables. c) von Neumann's mid-square method. d) Fibonacci and additive congruential generators. e) All of the above. - e) All of the above.
What are the most commonly used random number generators in practice today?
- Linear Congruential Generators What is the LCG general formula? - Xi = (aXi-1 + c) mod m Ri = Xi/m What is the period in a random number generator? - The amount of time until the LCG starts to repeat itself. Also called cycle length and you generally want a long one for a good generator. What can go wrong with LCGs? - 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? - BI = (BI-r + BI-q) mod 2 TRUE or FALSE? RANDU is a pretty good generator. - False
(c) Neither (a) nor (b). (d) Both (a) and (b). - (d) Both (a) and (b). If the ๐2 goodness-of-fit statistic, ๐20, is much greater than the relevant quantile ๐ 2 ๐ผ,๐โ1, 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! - a) Reject the goodness-of-fit test and declare that the PRNs are probably not uniform. What is a run? - A run is a series of similar observations. What is a run test? - 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. - True
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. - True TRUE or FALSE? The convolution method involves sums of random variables. - True Suppose that ๐1 and ๐2 are PRNs. What's the distribution of ๐1+๐2? Unif(0,2) Nor(0,2) Triangular(0,1,2) Exp(1/2) Exp(2) - Triangular(0,1,2) YES or NO? As in the notes, suppose that I want to generate a simple Unif(2/3, 1) via A-R. Suppose I generate a PRN ๐1=0.16. Do I accept ๐1 as my Unif(2/3, 1)? - No Suppose that ๐ is a continuous RV with p.d.f. ๐(๐ฅ)=30๐ฅ4(1โ๐ฅ), for 0<๐ฅ<1. Why is acceptance-rejection a good method to use to generate ๐? Because ๐ is always positive Because ๐ is almost normal Because ๐ is almost exponential
