Week 1

Question 1

What is a Random Number Generator (RNG)?

Answer 1

Question 2

What are the requirements for a RNG?

Answer 2

Question 3

What is the period length of a RNG?

Answer 3

Question 4

What is a LCG?

Answer 4

Question 5

What is a MRG

Answer 5

Question 6

What is a LFSRG?

Answer 6

Question 7

What is the Inverse Transform method?

Answer 7

Question 8

What is the accept-reject method?

Answer 8

Question 9

How do you find the most efficient implementation of the acceptence rejectance method?

Answer 9

Question 10

What is the Strong Law of Large Numbers?

Answer 10

Question 11

What is the Central Limit Theorem?

Answer 11

Question 12

What is the estimator for the sample average?

Answer 12

Question 13

How to create a confidence interval of the sample average?

Answer 13

Question 14

How to compute the sample variance? How to compute the standard error?

Answer 14

Question 15

What are some properties of the sample variance?

Answer 15

Question 16

What is the Monte Carlo algorithm?

Answer 16

Question 17

What do we need to verify after a Monte Carlo simulation?

Answer 17

Question 18

What are the components of a DES simulation?

Answer 18

• X is the set of all states
• E is the set of all events
• L : X → 2E is the active event function, aka event list
• φ : X × E is the transition function
• V = {Vn(e) : e ∈ E,n = 1,2,…} are the event life times
• P = {p(x, e, ·) : x ∈ X , e ∈ L(x)} are the transition probability distributions
• x0 is the initial state

Question 19

How to describe an (example) queing system?

Answer 19

Also describe:

L(x) is the list of active events in state x, called event list.
􏰉 These are the events that are currently scheduled to occur. 􏰉 Arrivals can always occur, thus α1 , α2 ∈ L(x) for all states x. 􏰉 A few event lists are

L(1, 0) = {α1, α2, β11}
L(1, 2) = {α1, α2, β11, β21, β22}
L(2, 1) = {α1, α2, β11, β12, β21}
L(2, 3) = {α1, α2, β11, β12, β21, β22} L(8, 5) = {α1, α2, β11, β12, β13, β21, β22}

and

State transition φ(x, e) = x′ means that when event e ∈ L(x) in state x occurs, the next state will be x′.

Examples

φ((1,0),α1) = (2,0)

φ((1,0),α2) = (1,1) φ((1,0),β11) = (0,1) φ((8,6),α1) = (9,6) φ((8,6),α2) = (8,7) φ((8,6),β13) = (7,7) φ((8,6),β21) = (8,5)

Question 20

What are the old and new events in DES?

Answer 20

Question 21

What is the clock structure of a DES model?

Answer 21

Question 22

How to find estimators of performance measures?

Answer 22

Question 23

What is Common Random Numbers (CRN)?

Answer 23

Question 24

What is the Paired t-test?

Answer 24

Question 25

What is a two-sample t-test?

Answer 25

Question 26

What is the difference between the Paired and two sample t-test?

Answer 26

The paired is when you have CRN.

Question 27

What is the two sample Welch-test?

Answer 27

Question 28

What is the Bonferri-equality?

Answer 28

Question 29

What is ANOVA? (Very long answer)

Answer 29

Question 30

What is post-hoc analysis?

Answer 30