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.
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. 26 of the text for the n event versions);
- the Axioms of Probability (p. 27);
- Propositions 4.1, 4.3, and 4.4 (pp. 29-31);
- first portion of Sec. 2.5 (pp. 33-34);
- definition of conditional probability ((2.1) on p. 59),
and reduced sample space viewpoint of conditional probability (see p. 3-1 of the course notes);
- multiplication rule (in box at bottom of p. 61,
and special case given by (2.2) on p.60);
- Bayes's formula (see p. 103);
- independent events (see definitions on pages 78 and 80);
- the law of total probability given by (3.4) in the box at the top of p. 72,
and the simple version of it given at the bottom of p. 3-5 of the course notes.
A dozen good problems to study:
- Problems 2 and 6 of HW 2
- Problems 1, 2, and 4 of HW 3
- Questions 2, 3, and the Bonus Question of Quiz 1
- Question 3 and the Bonus Question of Quiz 2
- Question 1 and the Bonus Question of Quiz 3
All of the HW problems and their solutions can be found in the Week 1, Week 2, and Week 3 folders of the course Blackboard site.
The solutions to the quizzes are also posted in the folders.
Here is a copy of an exam that I gave in Spring 2018, 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).
Here are solutions for this exam, showing proper justification for each of the answers.
(Note: The Spring 2018 exam has 11 parts, whereas your exam only has 6 parts. The Spring 2018 exam has some rather simple parts. While some of the parts of
your exam may be fairly simple, your exam also has one or more parts that may be more challenging than most of the parts of the Spring 2018 exam.)