Math 302

In the fall of 2013 I was the instructor for Math 302 -- Introduction to probability

Typed up lecture notes. (Final version.)

Some things you need to know about calculus.

More info in the course outline.

Homework assignments

Homework #1 --- Solutions #1

Homework #2 --- Solutions #2

Homework #3 --- Solutions #3

Homework #4 --- Solutions #4

Homework #5 --- Solutions #5

Homework #6 --- Solutions #6

Homework #7 --- Solutions #7

Homework #8 --- Solutions #8

Homework #9 --- Solutions #9

Homework #10 -- Solutions #10

Midterms

Midterm #1 --- Solutions

Midterm #2 --- Solutions

Material covered on the final:

To prepare for the final, you should study the lecture notes and the following sections in Ross (9th ed.):

Chapter 1: 1 -- 4, 6,

Chapter 2: 1 -- 5,

Chapter 3: 1 -- 5,

Chapter 4: 1 -- 7, 8.1, 8.2, 9,

Chapter 5: 1 -- 5, 6.1, 7,

Chapter 6: 1 -- 5,

Chapter 7: 1 -- 5, 7,

Chapter 8: 1 -- 3.

Extra practice:

Not to be handed in:
Homework #11 --- Solutions #11

The suggested problems below. It is unlikely that you will be able to finish the final in time if you haven't had enough practice, so make a lot of these. (And try at least for each one to figure out how you would solve them.)

Here are some links to other old finals (and solutions). These finals were written by different instructors, who may have had different priorities when they taught Math 302, so again, do not try to interpolate from these exams the precise structure of the final.

Link #1, Link #2, Link #3.

Suggested problems

It is important that you practice a lot, so I suggest that you try to make the following problems from Ross, 9th ed.:

Chapter 1: Problems: 1 -- 17, 21, 22, 24. Theoretical exercises: 2, 4, 8, 9, 11, 12b,c, 13, 16, 21, 23. Self-test: 1, 4 -- 12, 15 -- 17, 19.

Chapter 2: Problems: 1 --11, 13, 17 -- 20, 24, 27, 32 -- 34, 38, 41 -- 45. Theoretical exercises: 1 -- 5, 7, 11, 14. Self-test: 1 -- 7, 14, 15.

Chapter 3: Problems: 1, 2, 4, 5, 9 -- 20, 22 -- 24, 26, 28, 30, 32, 36 -- 38, 41, 44, 53, 54, 57 -- 60, 70, 73, 74. Theoretical exercises: 1 -- 3, 5, 6, 8 -- 10, 25.

Chapter 4: Problems: 1--10, 11(a), 13, 14, 18, 20, 21, 23, 25, 27 -- 30, 32, 33, 35, 38 -- 43, 46, 49 -- 61, 63, 64, 71, 74, 75, 79, 82, 83. Theoretical exercises: 5, 6,14, 19, 21, 28, 29, 36.

Chapter 5: Problems: 1 -- 8, 10 -- 19, 31 -- 33, 36 -- 40. Theoretical exercises: 1 -- 3, 5, 8 -- 13, 15, 21, 27, 29 -- 31.

Chapter 6: Problems: 1 -- 13, 16 -- 23, 28. Theoretical exercises: 5, 7(a), 9, 11.

Chapter 7: Problems: 1 -- 9, 30, 36 -- 40, 45, 46, 48 -- 51, 53-- 58, 61, 63, 75 -- 77. Theoretical exercises: 1, 6 -- 8, 23, 25, 26, 28, 29, 32, 35, 46, 48, 50.

Chapter 8: Problems: 1 -- 3, 4b, 5 -- 11.

Remarks about the treatment of Chapters 6 and 7 in Ross

Ross seperates the treatment of joint probability distributions and the expectation and variance thereof into two different chapters. We did not follow this approach, mainly because it takes too much time. The order in which we treated the material of chapters 6 and 7 roughly corresponds to this:

6.1, 6.2, 7.1, 7.2, 7.4, 6.3, 6.4, 6.5, 7.5, 7.7.

We already treated 7.3 when we were talking about general expectations, so that is also part of the course material. We will skip the remaining sections of chapters 6 and 7.