# MATH/STAT 394 - Probability I (Summer 2006)

### Announcements:

Answers: Practice problems, Lec3, Week4 q2 0.4869/0.0017, q4. 96, q5. 0.0228.
Sample Test. q2. 0.4866, q3. -.0787/1.245 (mean/var), q4. 0.0162, q5. 0.0793.

There will be extra office hours on July 18th, 9-11 in Padelford C301.

The final will be held in Sieg 134 (same as midterm), 8:30 to 10:30 am, July 19th.

The Monty Hall Problem
An applet
Some history
What Wikipedia has to say

This is an introductory undergraduate probability course. Probability is an incredible branch of mathematics, which allows us to model and gain understanding of the random phenomena we see in the world. We will begin with a look at the basic properties of probabilities : axioms of probability, independence, conditional probability. We also study combinatorics: essentially, you will learn how to calculate the probability of any possible hand in poker. We then look at random variables - both discrete and continuous, and their properties. We finish with a discussion of some basic limit theorems (law of large numbers, central limit theorem, Poisson limit theorem).

The prerequisites are: either 2.0 in MATH 126, or 2.0 in MATH 136.

Instructor: Hanna Jankowski

E-mail: hanna@stat.washington.edu
I have a request: when e-mailing me, please send plain text files and try to stay away from html - it's very difficult for me to read. Thanks in advance.

Office Hours: In my office, Padelford B220, after each lecture until noon (until July 17th). I will not have office hours after the test. However, I will most likely have additional office hours beforehand - these will be announced.

If you cannot make it to my office hours, please schedule an appointment.

Lectures will be held in SMI 407.

The text for this course is A First Course in Probability Theory, by Sheldon Ross, 7th Edition.

There is a copy of both the 7th and 6th edition of this text available for short-term loan from the Mathematics Research Library in Padelford Hall C-306. I have also requested that the text by John A. Rice, Mathematical Statistics and Data Analysis be placed on reserve there. It's a more advanced text, but I like the explanations.

There will be three assignments, a term test and a final in this course. The tentative schedule and (not so tentative) weighting scheme is as follows:

Assignment 1 : due Monday, June 26th, 7%

Assignment 2 : due Monday, July 10th, 7%

Assignment 3 : due Friday, July 14th, 7%

Note: all assignments are due at the beginning of each lecture. There are no exceptions. I do not accept late assignments.

Term test: Friday, June 30th, 35%

Final: Wednesday, July 19th, 44%

Note: all tests/final will be held during regular lecture times. I have requested a different room for these though - TBA.

### Course Policies etc.

• The tests are all closed book tests. You will probably need a calculator - only non-programmable calculators are allowed.
• There will be no make-up tests scheduled. In case of illness supported by medical documentation, your grade will be based on your other grades, pro-rated accordingly.
• Course work will be handed back during lectures. If you disagree with the mark you have received on a test, you should discuss the problem with the instructor within three days of when the work was returned.
• You are free to discuss your homework assignments with others, but you must write up your own solutions. I cannot stress this last part enough: not only is the right thing to do, but it's also how you learn the material. The assignments are due at the beginning of the class on the due dates. I do not accept late assignments.
• Attendance at all lectures is very important. I may not follow the text book at all times! Also, I may not follow the notation used in the text. You are required to learn the notations I give in class (and not that of the text).
• The best way to learn mathematics is to do mathematics. Make sure you keep up with the assigned (non-credit) excercises. Come see me if you have troubles. Notably, my assigned problems have a record of sneaking onto my tests and exams...

### Material Covered and Practice Problems:

In this section I will keep an ongoing list of the material we have covered, and the suggested practice questions attached to each lecture. It is imperative that you work through these on a timely basis.

We have covered the following sections/topics:

Week 1 :

• Sample spaces, working with sets, axioms of probability - roughly sections 2.1 - 2.4.
• Calculating probabilities: equally likely events and combinatorics - roughly 2.5, 1.1-1.5
• Conditional probability and independence - roughly ch.3

Week 2:

• Some longer problems, introduction to Random Variables, probability mass functions, classical examples of discrete rvs - 3.5, 4.1, and selective parts of ch.4
• More problems, review, more practice with random variables
• Midterm test!

Week 3:

• Continuous random variables, probability density functions, cumulative distribution functions - from ch.4 and 5
• More on cdfs, normal tables, expectation of a random variable
• More examples on expectation of a random variable, expectation of a function of X, variance and standard deviation

Week 4:

• More on variance, independence of random variables.
• mean and variance of sums of independent random variables, Poisson Limit theorem
• Central Limit Theorem and applications.

Practice (non-credit - do not hand these in) problems:
Week I
Week II
Week III
Week IV