# STAT 134: Concepts of Probability (Fall 2012)

Finals week: December 10 - 14

Office Hours (Aldous): Wednesday 2.00 - 4.00 in 351 Evans.

FINAL EXAM Friday 11.30 - 2.30, room 10 Evans

Note The last homework may not be graded by Wednesday. Please come early to the final exam if you wish to pick up your homework.

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Instructor: David Aldous (aldous@stat)

Class time: MWF 12.00 - 1.00 in room 60 Evans

GSI Mu Cai (mucai@stat.berkeley.edu)

Attendance in supplemental section 101 or 102 is strongly recommended but not required. These meet Fridays, 2.00-3.00 (sec 101) and 3.00-4.00 (sec 102) in room 330 Evans.

Check the Student Learning Center STAT 134 page for their study group times and drop-in times.

Textbook Probability, by Pitman.

If you are taking this course, I suggest you read (and maybe print out) right now

Obviously these schedules might be changed as the semester progresses.

Some time you will want to print out

Practice Midterm and solutions. Note only questions 1, 2, 4 have been covered so far in this course.

The text also contains practice exams.

Here are PDF versions of another textbook and lecture notes available online

These are aimed at math majors but are a good source of examples and exercises for STAT134.

### Office Hours

(Aldous) Thursdays 2.15 - 3.45 in 351 Evans

(Mu Cai): Monday 2-3pm Evans 307, Thursday 2-4pm Evans 307, Friday 4-5pm Evans 330.

If you email us put "STAT 134" in subject line.

### Lecture topics

A few of the early lectures use slides -- these will be posted after the lecture. Some slides are deliberately incomplete, in that a problem stated in the slides is to be solved on the blackboard.

(Chapter 1)

Lecture 1 (F 8/24). Introduction.

Lecture 2 (M 8/27). Proportions, conditional probability examples, Monty Hall.

Lecture 3 (W 8/29). Independence, examples with independence, Bayes rule.

Lecture 4 (F 8/31). Examples using Bayes rule. Birthday problem, illustration of calculus approximation. Probability distributions.

(Chapter 2)

Lecture 5 (W 9/5). Binomial distribution; examples.

Lecture 6 (F 9/7). Normal approximation to Binomial -- the big picture.

Lecture 7 (M 9/10). Normal approximation to Binomial -- examples. Confidence intervals

Lecture 8 (W 9/12). Confidence intervals and opinion polls. Poisson Approximation.

Lecture 9 (F 9/14). *** NO CLASS ***

Lecture 10 (M 9/17). Poisson Approximation; hypergeometric distribution.

Lecture 11 (W 9/19). A genetics example, illustrating Bayes updating.

Lecture 12 (F 9/21). Random variables.

Lecture 13 (M 9/24). Joint distributions for 2 random variables.

Lecture 14 (W 9/26). Expectation: conceptual and mathematical properties.

Friday September 28. MIDTERM 1 (covers Chapters 1 - 2).

Lecture 15 (M 10/1). Expectation: conceptual and mathematical properties (continued).

Lecture 16 (W 10/3). Variance and standard deviation: conceptual and mathematical properties.

Lecture 17 (F 10/5). Variance for Binomial. Poisson and Geometric. Collector's problem. [Inequalities]. Standardization.

Lecture 18 (M 10/8). Normal Approximation (the central limit theorem) for sums and averages.

Lecture 19 (W 10/10). Examples of Normal Approximation. Poisson distribution: more math facts,

Lecture 20 (F 10/12). Poisson distribution: use in modeling, use for approximate calculations. Sudden death games.

Lecture 21 (M 10/15). Variance for counting RVs. Inequalities. Random point in spatial region.

Lecture 22 (W 10/17). Continuous RVs; distribution functions and density functions.

Lecture 23 (F 10/19). Uniform and normal densities. Poisson random scatter example.

Lecture 24 (M 10/22). Poisson arrival process; model and math properties.

Lecture 25 (W 10/24). Hazard rates; distribution of Y = H(X), change of variable formula.

Lecture 26 (F 10/26). Examples, Cauchy distribution, linear transformatins. Simulating X = F^{-1}(U).

Lecture 27 (M 10/29). Rejection sampling. Order statistics and beta distribution.

Lecture 28 (W 10/31). Alternative formula for expectation. Gambling on a favorable game (intro to portfolio theory). See Chapter 4 of these notes for a little more material.

Lecture 29 (F 11/2). Joint densities.

Lecture 30 (M 11/5). Examples with joint densities.

Lecture 31 (W 11/7). Densities for sums, quotients etc.

Friday November 9. MIDTERM 2 (covers Chapters 1 - 4).

Lecture 32 (W 11/14). Independent Normal RVs.

Lecture 33 (F 11/16). Conditional distributions and expectations: discrete case

Lecture 34 (M 11/19). Conditional distributions and expectations: continuous case

Lecture 35 (W 11/21). Linear prediction (regression), correlation, covariance.

Lecture 36 (M 11/26). Bivariate Normal distribution.

Lecture 37 (W 11/28). Examples and interpretation of correlation; sampling. Review examples with independent Normals.

Lecture 38 (F 11/30). Example (auto insurance) to illustrate conditional and joint distributions.

Lecture 39 (M 12/3). Review examples: exams on same day; buying every Lotto combination; newsboy problem.

Lecture 40 (W 12/5). Open questions.

Friday December 14, 11.30-2.30, room 10 Evans FINAL EXAM (covers Chapters 1 - 6).