review for 1st midterm, STAT 544

Information Pertaining to the 1st Midterm Exam

Basics

It'll be a closed book and closed notes exam. You can use a calculator, but not a computer. I'll leave room on the exam for you to work the problems, so you won't need to bring paper or an exam book. All you'll need is a pencil and perhaps a calculator (in addition to a mastery of the material).

Please click here to see the instructions for the exam, which contains a description of the exam. For examples of what I mean by defining events in solutions of problems, in the course notes see the last example on p. 3-6, the example in the middle of p. 3-8, and the last example on p. 3-10. As for thorough justification in your solutions, if you go from the probability of an intersection of two events to the product of their two probabilities, you can write ind. over the = sign to indicate that you're using the independence of the two events, and if you go from the probability of a union of two events to the sum of their two probabilities, you can write mut. excl. over the = sign to indicate that you're using the fact that the two events are mutually exclusive. Similarly, if you use Bayes's formula or one of De Morgan's laws, you can write Bayes or De Morgan over the = sign.

I'll give you about 75 minutes for the exam, and teach for about 75 minutes (continuing in Ch. 5).

What to Study

The exam will cover Chapters 1, 2, and 3, except for Sections 1.6, 2.6, and 2.7. Emphasis will be on the main important parts of each chapter. Messy details, novel lesser-used results, and complicated things like the gambler's ruin problem will not be emphasized. There won't be any problems that just use Ch. 1 material, but important Ch. 1 results and principles may be needed for solving problems based on the Ch. 2 and Ch. 3 material.

Some really important things are:

combinations (see pp. 5-6);
De Morgan's laws (see p. 2-2 of the course notes for the 2 event versions, and p. 25 of the text for the n event versions);
the Axioms of Probability (p. 26);
Propositions 4.1, 4.3, and 4.4 (pp. 28-30);
first portion of Sec. 2.5 (pp. 32-36);
definition of conditional probability ((2.1) on p. 57), and reduced sample space viewpoint of conditional probability (see p. 3-1 of the course notes);
multiplication rule (in box near bottom of p. 59, and special case given by (2.2) on p.58);
Bayes's formula (see p. 97);
independent events (see definitions on pages 75 and 77);
the "valuable identity" given about 50% down the page on p. 97, and the extension of this identity using a partition F₁, F₂, ..., F_n instead of just F and F^C (see top half of p. 3-7 of the class notes).

A dozen good problems to review:

1 of HW 1
3 of HW 1
8 of HW 1
1 of HW 2
2 of HW 2
3 of HW 2
4 of HW 2
5 of HW 2
6 of HW 2
7 of HW 2
2 of HW 3
4 of HW 3

All of the HW problems and their solutions are linked to from the homework web page.

Here is a copy of an exam that I gave in Spring 2014, which is somewhat similar to the exam I'll give you. I strongly suggest that you print out this exam and take it for practice under exam conditions (75 minutes, closed book and notes). I'll supply you with a copy of the solutions to this exam in class.