Midterm Exam

Information

The midterm will be in class on Thursday, February 25. You may bring:

• One sheet of notes (8.5" x 11", you may use both sides)
• One non-programmable calculator

You will be provided any statistical tables you may need (e.g. for looking up critical values for Kolmogorov-Smirnov or Chi-Squared, or for looking up the area under a standard normal curve):

• Chi-Squared Table
• Standard Normal Table
• Kolmogorov-Smirnov Table

Practice Questions

Practice questions are available via the Review page. You may also find it helpful to review the examples done in lecture (available in the lecture slides).

Material to Review

The midterm covers the following topics:

• Overview of Simulations (slides, slides)
  • Simulation fundamentals
  • Terminology
  • How to represent time
  • When to use (or not use) simulations
• Probability Distributions (slides, slides)
  • Basic probability, e.g. Bayes' theorem, joint and conditional probabilities
  • Terminology, e.g. what's the difference between a sample space and a probability distribution?
  • Calculating a probability distribution from observed data
  • Calculating expected values and variances
  • All of the distributions discussed in Review of Probability Distributions; know their pdf/pmf, cdf, expected value, variance, and any other properties about them
• Random Number Generation (slides)
  • Generating random numbers from the continuous uniform distribution (U[0, 1) using Linear Congruential Generators
  • Testing for uniformity of numbers generated according to U[0, 1) using Kolmogorov-Smirnov Test and Chi-Square Test
  • Testing for independence of numbers generated according to U[0, 1) using Runs Tests and Autocorrelation Test
• Random Variate Generation (slides)
  • Generating random variates using Inverse Transform Method
  • Generating random variates using the Accept/Reject Methods
  • Generating random variates using special properties of the distributions

Survey Results

Of the 17 students who completed the survey, a majority (10) voted to have the midterm during the first half of the 2/25 class and a plurality (8) voted to have the review session on the second half of the 2/18 class. A majority of the respondants (13) want a lecture-style review session, where topics and questions will be submitted through another survey and will be discussed during the review session. This second survey is now available through CourseWeb. If you want additional review or prefer to have the review closer to the midterm, my office hours are available before and after class.

Questions about the Midterm

• "What will the format be? Mostly problem solving, possibly multiple choice or short answer?"
  "What's the format of the exam?"
  "Should we expect the questions on the exam to be similar in difficulty and format of the review questions? Similar in difficulty and format to the first homework?"
  • The exam will mostly be problem solving and short answer. See this example midterm (note: this example only shows the kinds of questions to expect; it does not show the distribution of topics that will show up on the midterm).
  • The exam questions will be similar in difficulty and format to both homework 1 and most of the review questions (don't expect as many True/False and multiple choice though).
• "Will you be posting answers for the review questions?"
  • No. However, if you want to check your answers, you can email me your answers or visit office hours.
• "Will you be posting a practice midterm exam with answers?"
  • There is an example midterm, but it's only an example to show the kinds of questions to expect; it does not show the distribution of topics that will show up on the midterm. It would be more productive to use the review questions. Answers will not be posted for the example midterm, but if you want to check your answers you can email me your answers or visit office hours.
• "Are there answers/solutions for the Homework 1 probability problems? It'd be great to have an idea of exactly how to do some of the harder questions."
  • Yes, they're now available at the bottom of the Homework 1 page.
• "I know you mentioned this in class, if we choose to use a graphing calculator (TI-84) for the exam, will that be okay if you check it prior to beginning the exam?"
  • That's fine. Anyone who wants to use a graphing calculator should show up early (5:20) so the calculator can be checked.
• "Will the midterm be more focused on specific topics or will the test questions be evenly distributed  amongst all the material we've learned so far?"
  • It will be approximately evenly distributed across the topics covered. Topics that require a spark of luck/insight to solve (e.g. Polar Method for Random Variate Generation of N(0, 1) or determining the bounding curve in the Accept/Reject method) either will not appear or that luck/insight will be provided for you.
• "I haven't done much calculus in the last five years, and it would be really helpful to give us some more of an idea of what we are responsible for, and to provide some more examples of the material we need to know."
  • You should be able to:
    • take integrals and derivatives of polynomials
    • do algebra
    • basic logarithmic identities
    • basic exponentiation properties
    • find the global maximum of a function
    • basic trig function definitions

Review Session Topics/Questions

Continuous Probability Distributions

• "I would like to go over more practice problems. I have been trouble identifying which probability distribution applies to a problem. A general overview of all probability distributions would help a lot!"
• "Approaches to using the different distributions. In general, a chance to feel more comfortable using these distributions and to know what to use. A lot of the continuous distributions are new or at least relatively unfamiliar to me, so these are definitely a topic that would be helpful to go over."
• "It would be really helpful to cover some more examples using the probability distributions, and to practice general strategies for those problems."
• "Regarding topics to focus on during review, I would especially like to review some of the more challenging probability distributions (poisson, erlang, gamma) as well as tactics for determining when to use pdf/pmf or cdf.  I would also appreciate going through an example of autocorrelation. Thanks!"
• "One of the areas I was hoping we would cover in class is a general overview of deciding how to choose the right distribution equation for calculating a probability, given a scenario. Specifically, I can pick out pretty well which type of distribution we should use but then get confused about selecting either the PDF or CDF equation."

Random Variate Generation

• "I would appreciate going over math involved in calculating these numbers and a review of the usage of these techniques. It would be especially nice to cover the more math-intensive parts."
• "I am worried about not being able to solve the calculus parts of these problems on the test. So possibly going over problems with a lot of calculus may ameliorate this issue."
• "Also, I would be grateful if we went through another example or two for the "special properties" section from last week's random variates lecture, particularly the naive, improved, and efficient methods for sampling from N(0, 1), which I believe are part of the polar coordinate method."

Discrete Probability Distributions

• "Like my issues with the Continuous Probability Distributions I still have trouble identifying the appropriate distribution that applies to a problem. Again, I think that a general overview of these distributions would help greatly!"
• "Like for continuous distributions, it would be helpful to review the usage of the discrete distributions after negative binomial and to see some more examples."