About the Final Exam: STA256f19

The following information applies to the 2019 regular final exam. The special deferred exam is different. You are strongly encouraged to take the regular exam.

There are 13 questions, on 13 pages including the cover page. The current posted formula sheet will be provided. Many of the questions have words like "Find" and "Prove" and "Show" and "Derive," but some questions have numerical answers. Bring a calculator. There are no multiple choice questions.

In this course, the homework problems tell you what we want you to be able to do. So the best way to prepare for the exam is to make sure you can do the homework problems. Ideally you should re-do all the homework problems, but beware of trying to do it by starting at the beginning and then running out of time. The exam is comprehensive, but there is more weight on middle and last part of the course, particularly the material on convergence in Assignment 10. Questions like the ones in Assignment 10 typically require an understanding of concepts and methods from earlier in the course as well as the limits part, so they make good exam questions. There are no questions directly from Assignment 1; that was review.

Another good source of practice is to treat the in-class sample problems as homework problems with solutions. Try them first without peeking at the solutions. Tests from this year with solutions are posted. Last year's tests and exam are posted too. You will see that the questions are very predictable, and very like the homework. However, last year's final exam was light on the last unit. We went too slowly at the beginning and ran out of time. Exams from 2017 and earlier are from different instructors. The questions I have looked at are quite good, but in the past, STA256 covered a lot less material than we did. In some years they did not even get to moment-generating functions. What we did this year is pretty much the North American standard. Next year the term tests will be outside of lecture time, and it will be possible to spend a bit more time on the Central Limit Theorem. That will be ideal.

Everything on the exam this year is predictable, but not everything that's predictable is on the exam. The first draft was too long, and we cut out some things that you would legitimately expect to see. These topics are important and you should be rewarded for studying them and knowing them. Their omission is a defect in the exam, but at least you saw that stuff in the term tests. And, it's important for the exam not to be so long that the average student cannot finish it. In fact, now I think that maybe the exam is a bit short. There is a quick way to do many of the questions if you see it. If something seems too easy, it's probably not too easy; you just thought of the right way to do it.

Here's a bonus: something that's not going to be on the exam. From the beginning of the course, I was planning to put Question 19 from Assignment 10 directly on the exam. It's like the proof of the Central Limit Theorem, but not as long and messy. However, we did not get to the proof of the Central Limit Theorem, and also, though question 19 is also a sample question, I did not actually lecture it because we ran out of time. So instead of being a reasonable question, it now would be unreasonable. It's not on the exam.

Here are a few more pieces of advice.

• Answer the question that is asked, not a similar question from homework. We are looking for evidence of understanding, and a memory dump does not fall into that category.
• Your answers will be taken literally. Don't write stuff you don't mean. For example, if you write that a random variable is equal to its probability density function, that's a serious mistake. Also, if you want the marker to disregard something, scratch it out. If you write something irrelevant and it's correct, it can't hurt you. If it's wrong, you will lose marks.
• Don't force the answers to proofs and derivations. Sometimes, a student is asked to show something and it is not working out. The temptation is to either make a deliberate mistake or an incredible jump of reasoning, write the final conclusion and say "proved." This is fraud. If you try to fool us and it works, fine. If we detect it, you will get a zero for the entire question (or part of a question, if it's part c or something).
• Sometimes, a little mistake can lead to something clearly impossible, like a negative probability or a negative probability density function. If this happens to you, don't just let it go by. Write something like "I must have made a mistake somewhere. Probabilities can't be negative." In that case we will realize that you know what's going on, and you might get only a very small deduction or no deduction at all for the mistake that caused the problem. On the other hand, if you give us a negative probability with no comment, we will assume that you don't understand.
• Be familiar with the formula sheet. It's actually a good summary of what we have covered in the course. The rule is that you may use anything on the formula sheet unless you are directly asked to prove it.

Finally, remember that if you score at or above the class median on the final exam, you will pass the course regardless of what happened on the term tests.