Download ISYE 6644 SUMMER FINAL EXAM QUESTIONS AND ANSWERS 2026/2027 and more Exams Statistics in PDF only on Docsity!
ISYE 6644 SUMMER FINAL EXAM QUESTIONS AND
ANSWERS 2026/
If f(x, y) = cxy for all 0 < x < 1 and 1 < y < 2, where c is whatever value makes this thing integrate to 1, then X and Y are independent random variables - CORRECT ANSWER - TRUE. (Because f(x, y) = a(x)b(y) factors nicely, and there are no funny limits.) In our Arena Call Center example, it was possible for entities to be left in the system when it shut down at 7:00 p.m. (even though we stopped allowing customers to enter the system at 6:00 p.m.). - CORRECT ANSWER - TRUE โ because of the small chance that a callback will occur. An entity can be scheduled to visit the same resource twice, with different service time distributions on the two visits! - CORRECT ANSWER - TRUE Arena has a built-in Input Analyzer tool that allows for the fitting of certain distributions to data. - CORRECT ANSWER - TRUE The Kolmogorov-Smirnov test can be used both to see (i) if data seem to fit to a particular hypothesized distribution and (ii) if the data are independent. - CORRECT ANSWER - FALSE. (It's just a goodness-of-fit test.) Welch's method is a graphical technique to estimate truncation (initialization bias) points for steady-state simulation. - CORRECT ANSWER - TRUE If you are using a ranking-and-selection procedure and two competitors happen to fall within the indifference-zone, then you don't really care too much which one you end up selecting. - CORRECT ANSWER - TRUE. That's why it's called the IZ!
TRUE or FALSE? Sequential ranking-and-selection procedures are designed to stop early if one alternative seems to be way out in front of the others. - CORRECT ANSWER - TRUE Suppose, when designing a ranking-and-selection procedure, you have decided to increase the desired probability of correct selection compared to a previous run of the procedure. What can you expect? (a) Sample sizes that are about the same (b) Larger sample sizes (c) Somewhat lower achieved Pr(CS) (d) A larger indifference zone (e) Lower confidence in your selection - CORRECT ANSWER - b In Arena, you can use a single DECIDE module to route customers to that one of four servers having the smallest queue. - CORRECT ANSWER - TRUE TRUE or FALSE? In Arena, you can use the expression EXPO(3) to generate exponential interarrival times having a mean of 1/3. - CORRECT ANSWER - FALSE. The mean of an EXPO(3) is 3. TRUE or FALSE? In Arena, an alternative expression to generate exponential interarrival times having a mean of 1/3 is - (1/3)*LN(UNIF(0,1)) - CORRECT ANSWER - TRUE. This is the Inverse Transform Method to generate an observation coming from Exp(ฮป = 3). TRUE or FALSE? In Arena, it is possible to set the maximum capacity of a queue from within a SEIZE module. - CORRECT ANSWER - FALSE. It is only possible to set a maximum queue capacity from within a QUEUE block found in the Blocks template. 2 TRUE or FALSE? In Arena, the expression NORM(-1,2)+NORM(3,2) has the same distribution as the expression NORM(2,4) - CORRECT ANSWER - FALSE. The above expression evaluates to NORM(2,โ 8) since, in Arena, NORM(x,2) corresponds to a normal random variate with a mean of x and a standard deviation of 2; so the variance of this random variable is 22 = 4.
TRUE or FALSE? The Arena Call Center model discussed in class used a nonhomogeneous Poisson process arrival process (with rates varying throughout the day). - CORRECT ANSWER
- TRUE Regarding Linear Congruential Generators (LCG's), select the statement that is correct. - CORRECT ANSWER - Both full periodicity and cycle length properties should be considered when choosing a good LCG. We are testing a new medication. Our null hypothesis, H0, is the assumption that the medication is safe. If we reject this null hypothesis but the medication is actually safe, what type of error have we committed? - CORRECT ANSWER - Since we have incorrectly rejectedthe null hypothesis of safety, we have committed a Type I error TRUE or FALSE? In Arena, it is not possible use a single DECIDE module to randomly route customers to one of three or more destinations. - CORRECT ANSWER - FALSE TRUE or FALSE? In Arena, you can use the expression EXPO(3) to generate exponential interarrival times having a mean of 3. - CORRECT ANSWER - TRUE TRUE or FALSE? In Arena, an alternative expression to generate exponential interarrival times having a mean of 3 is - (1/3)*LN(UNIF(0,1)) - CORRECT ANSWER - FALSE. This is the Inverse Transform Method to generate an observation coming from Exp(ฮป = 3), which has a mean of 1/3. TRUE or FALSE? In Arena, it is possible to set the maximum capacity of a queue from within a QUEUE block found in the Blocks template. - CORRECT ANSWER - TRUE. In fact, it's pretty much the only way. What is the variance of the random variable given in the Arena expression NORM(- 1,3)+NORM(3,4)? - CORRECT ANSWER - : In Arena, NORM(x, y) corresponds to a normal random variate with a mean of x and a standard deviation of y. So the variance in question is 3 2 + 42 = 25.
TRUE or FALSE? In Arena, it is possible to grab more than one resource at a time in a PROCESS module - CORRECT ANSWER - TRUE TRUE or FALSE? In Arena, it is possible to change the priority in which entities get processed by a resource - CORRECT ANSWER - TRUE TRUE or FALSE? In Arena, it is possible to use a single RELEASE module to release multiple different resources - CORRECT ANSWER - TRUE. We observed this in the ReleaseHospitalRoomLater demo in HW What is the distribution given by the Arena expression UNIF(0,2)+UNIF(0,2)? - CORRECT ANSWER - Tria(0,2,4) TRUE or FALSE? An Arena ASSIGN module can be used to assign values to attributes but not variables. - CORRECT ANSWER - FALSE. It can be used for both Suppose X is a discrete random variable that can take on four possible values: โ 2, 1, 4, and 7. The associated probabilities are, respectively: 0.1, 0.3, 0.2, and 0.4. Find an expression in Arena to generate one observation coming from this p.m.f. - CORRECT ANSWER - DISC(โ2, 0.1, 1, 0.4, 4, 0.6, 7, 1) Suppose there are 3 people in the line called joe.queue and 2 people in the line called tom.queue. What is the value of the following Arena expression? NQ(tom.queue) โ NQ(joe.queue) + (TNOW < โ1) - CORRECT ANSWER - The logical expression (TNOW < - 1) is false (since time is always at least 0). Thus, NQ(tom.queue) โ NQ(joe.queue) โ (TNOW < โ 1) = 6 + 0 = 6. TRUE or FALSE? The Arena Call Center model discussed in class restricted all servers to one specialty product each. - CORRECT ANSWER - FALSE. The use of resource sets allowed certain servers to work on multiple products.
If X1,... , Xn are i.i.d. Exp(1/9), what is the expected value of the sample variance S 2 ? - CORRECT ANSWER - E[S^2 ] = ฯ^2 = 81. Find x such that e 2x = 1/x. (Get within two decimals) - CORRECT ANSWER - Bisection search quickly reveals that x is about 0. TRUE or FALSE? The square root of the sample variance is unbiased for the standard deviation - CORRECT ANSWER - FALSE. (E[S 2 ] = ฯ 2 ; E[S] = ฯ.) Which is usually a better way to deal with initialization bias in steady-state simulation analysis: (i) make an extremely long run to overwhelm the bias, or (ii) perform truncation? - CORRECT ANSWER - Truncate If W(t) is a standard Brownian motion process and a < b, find Pr(W(a) < W(b)). - CORRECT ANSWER - W(a) โ W(b) is normally distributed with mean 0. This immediately yields a probability of 1/2. Suppose I use the method of overlapping batch means with sample size n = 10000 and batch size m = 500. Approximately how many degrees of freedom will the resulting variance estimator have? - CORRECT ANSWER - Denote b = n/m = 20. You get approximately 3 2 (b โ 1) = 28.5 d.f. (Will also accept 3b/2 = 30 or anything reasonably close.) Suppose that I'm interested in selecting the most popular television show during a particular time period. What kind of selection problem is this โ (a) normal, (b) multinomial, or (c) Bernoulli? - CORRECT ANSWER - b
