The following is simply a conveniently formatted list of learning goals. More likely than not, some might be hard to assess through a quiz or exam. Students should prioritize their studying based on:

- how much time in lecture was spent discussing or understanding the topic,
- how much the topic was stressed in learning group assignments
- and the student's comfort level with the topic

# Assessable Learning Goals covered for Exam 1

Know the rules for presenting **discrete** and **continuous** data relationships (scatter plots vs connected dots).

Know how to use *accept/reject* techniques for uniformly random (geometric) point generation.

Know how to write Monte Carlo simulations for estimating the *Pr(A)* of an event A.

Know the pitfalls associated with common (naive) methods of random point generation.

What unique characteristic of a system or simulation makes it ** Monte Carlo**?

Know the tell-tale feature(s) of spatial plots produced by faulty point generation algorithms.

When randomizing points in a circle without accept/reject, how should the radi *r* be chosen using *Random()*?

Why is it important to use multiple seeds and many replications in Monte Carlo simulations.

How do you ** apply** pRNG streams to achieve

**in simulation experiements?**

*variance reduction*"Good" pRNGs requiring *k* bits to hold values of their state space *S* have a **period** approximately how large?

Understand that skewed results are obtained from SIS simulations (w/ delivery delays) with **syncronized** demand and delay random sequences.

Why is breaking up a modern, large period pRNG into **streams** avoided?

What (arithmetic) pRNG properties did the thieves take advantage of in electronic poker games?

Explain the values *a*, *m*, *g()* and *x0* in a (Lehmer) PMMLCG; how is the next *Uniform(0,1)* random value calculated?

Given *a* and *m* (*a* a full period multiplier), find the smallest and largest floating point values between 0 and 1 that can be generated.

How is a (sub)stream of a Lehmer pRNG created?

How is an *x _{i+1}* value converted from an integer to a real number in the interval

*(0,1)*?

What does the pRNG API routine *Random()* provide to a simulation writer?

What is a **full period multiplier** and why is it important to Lehmer pRNGs?

Explain what "random numbers fall mainly in the planes" means.

What is the geometric interpretation of multiple Lehmer pRNG streams?

What is special about **outliers** in the context of computer simulation results?

What are empirical CDFs? How are they better than histograms for assesing a data distribution?

How does serial correlation affect estimated mean and standard deviation?

What is the difference between ** serial** and

**correlation?**

*paired*What is ** autocorrelation** and

**? Why is autocorrelation important in DES?**

*autocorrelation lag*What is positive (and negative) serial correlation? Cite a positive serial correlation example from the SSQ model.

Know the general form of the integral equations for CRVs (average and deviation calculations).

Know what constitutes a **histogram** and how it is connected to CDFs.

How is the height of a continuous histogram bin calculated?

Know the general approach to binning continuous data, about how many bins are needed for a sample of `n`

?

How is the approach of MSOD regression lines different than the approach taken for conventional "least squares" regression lines?

What is a **mean-square orthogonal-distance** (MSOD) linear regression line?

Why are MSOD regression lines more suitable for DES?

Why don't we use standard statistical linear regression lines for DES results?

Given Welford's discrete and integral mean and variance equations (Thms 4.1.2, 4.1.4), be able to apply them to a set of data.

Know that **Welford's Equations** exist, why they are superior to the "one-pass" algorithm common in statistical texts.

Know which of the two (** non Welford**) standard equations for calculating

*s*or

^{2}*s*is flawed.

DES people don't need integrals and anti-differentiation when integrating. Why not?

Given Welford's covariance equations (Thm 4.4.3), be able to apply them to a set of paired data *(u,v)*.

Know that ** uniform arrival times** and

**are not the same thing.**

*uniform interarrivals*Know that ** valid** computer simulations

**produce outliers. End of discussion.**

*do not*What are *consistency checks*? How can they be used in V&V?

What are the authors' five phases of simulation development?

What is simulation validation?

What is simulation verification?

What is the computational model of a simulation?

What is the conceptual model of a simulation?

What is the specification model of a simulation?

Name two acceptable ways to validate a simulation.

When can a particular phase (concept, specification, computational, v&v) of simulation development be skipped?

Know how to calculate **traffic intensity** and its connection to **service rate**.

Understand how a FIFO SSQ simulation can be written in a simple while loop and how *a_i* and *s_i* can be manipulated for simple experiments.

Understand the canonical SSQ and appreciate its broad application to computer simulation.

Know the *Equilikely(a,b)* random variate: the meaning of its parameters, pmf, and CDF.

Know the *Exponential(mu)* random variate and the interpretation of its parameter *mu* in the context of arrival times.

Know the *F(x) inversion* technique for constructing random variates. What is the requirement on *F(x)*?

Know the *Uniform(a,b)* random variate: the meaning of its parameters, pdf, and CDF.

Understand the problems with the **often used and always flawed** `RandomInteger() mod SIZE`

programming pattern.

What does the parameter *u* in random variates represent? Computationally, how do we get a value for *u* in code?

Know the difference between a **random number** and a ** random variate**.