Exam Content
The exam will cover selected material from class.
- Topic 1 Point Estimation I
- Bias of an Estimator
- Variance of an Estimator
- MSE of an Estimator
Topic 2 Point Estimation II
- Topic 3 Point Estimation III
Method of Moments
- Maximum Likelihood
- Fitting a Probability Model
- Topic 4 Confidence Intervals
Confidence Intervals for Means
Confidence Intervals for Proportions
- Confidence Intervals for Variances
- Confidence Intervals for Difference of Means
- Confidence Intervals for Difference of Proportions
Topic 5 The Bootstrap
Bootstrap Confidence Intervals
The sample()
function
The quantile()
function
- Topic 6 Hypothesis Testing
- Main Ideas
- Hypotheses, Significance, Test Statistics, P-Values, Power, Etc.
- Large Sample Tests for…
Means
Proportions
Difference of Means
- Difference of Proportions
- Smalls Sample Tests for…
Means
- Difference of Means
-
Variances
- Topic 7 Nonparametric Testing
The Sign Test
Permutation Tests
Comparison to Parametric Testing
- Topic 8 ANOVA
- F-Test
- Contrasts
Multiple Testing
- Topic 9 Categorical Data
- Topic 10 Bayesian Statistics
- Priors, Likelihoods, and Posteriors
- Bayes Estimators
- Credible Intervals (Using
qbeta()
)
- Bayesian Hypothesis Testing (Using
pbeta()
)
Questions on the Exam will be similar in style to those on Homework and Practice Problems.
Advice for Studying
Like most mathematical courses, the most important thing you can do to study is exercise (practice) as much as possible. You have two resources for practice exercises which will be very relevant to the exam:
- Homework
- Practice (Posted with each Homework. Will be added to as we approach the exam.)
You have the solutions for these items, but when using these effectively, you should attempt all problems before referencing the solutions. Reading a solution and thinking “I know this” is very different from starting with a blank page and writing a solution. You won’t have solutions on the exam. You will have a blank page.
Creation of your notes sheet should be a by-product of practicing. Anything you needed to reference in notes when doing the exercises should be written on your notes sheet.
Time spent reading notes is far less valuable than time doing practice exercises. Many students believe reading the textbook or notes is useful for studying. In fact, time spent reading for the sake of reading is completely wasted. The notes and textbook should be used to help you eliminate gaps in your understanding which are discovered through practice problems. (But often, the solutions will be more directly useful.)
Some very bad ideas:
- Copying a notes sheet of another student. Writing the notes sheet is a very helpful study tool. The act of simply writing down a definition will make it easier to remember, thus cost you less time during the exam.
- Writing entire problems from homework or practice on a notes sheet. Students who rely on this strategy almost always run out of time on the exam. The notes sheet replaces needing to memorize formulas and definitions, not how to do every type of problem.
- Pulling an all-nighter.
For some general advice on being a good student, take a look at this post from Andrej Karpathy. (Andrej was a very successful CS student, now well known in the Deep Learning community.) I don’t necessarily agree with everything he says, but he has a very good perspective.
Frequently Asked Questions
How many problems are on the exam?
- This question is irrelevant since each problem could have an arbitrary number of parts. A one problem exam could easily be written to be longer than a ten problem exam.
How long will it take to do the exam?
- If you are well prepared and manage your time efficiently: Under 105 minutes.
- If you are ill prepared or manage your time poorly: Over 105 minutes.
- You should not focus on this. Focus on practicing and being able to do questions of the types you’ve seen on homework. Let me worry about this. And believe me, I worry about this a lot.
Is there a practice exam?
- No, but you have a large number of practice problems, some of which, came from old exams.
Will the exam be curved?
We got our grades back, now will the exam be curved?
- No. Unless you want it to curved to a normal distribution with a mean of 75. In which, case, sure, that would make my life easier.
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