Roman Vershynin, Department of Mathematics, UC Irvine

**Email:** rvershyn "at" uci "dot" edu

**Office hours:** Mon, Wed 3:00 - 3:50pm in 540D Rowland Hall

Adrien Peltzer, Department of Mathematics, UC Irvine

**Email:** apeltzer "at" uci "dot" edu

**Office hours:** Tu 1:00 - 2:00, Wed 1:00 - 3:00pm in 532 Rowland Hall

**Lectures:** MWF 4:00 - 4:50pm in DBH 1200

**Discussion:** TuTh 8:00 - 8:50am in RH 114

**Course description:** Basic concepts of probability are introduced,
and applications to other sciences are noted. The emphasis is on concepts,
calculations, derivations and problem-solving.
The course covers foundations of probability theory including,
conditional probabilities, independence, discrete and continuous random variables.

**Prerequisites:** Calculus and Linear Algebra. Detailed prerequisites can be found here.

**Textbook:** S. Ross, First Course in Probability, 9th edition. ISBN: 9780321794772

The course grade will be determined as follows:

**Homework:**10%. One homework with the lowest score will be dropped. Solutions will be collected every Thursday. Late homework will not be accepted. You are welcome and encouraged to form study groups and discuss homework with other students, but you must write your solutions individually.**Quizzes:**15%, every Thursday. One quiz with the lowest score will be dropped.**Midterm Exam 1:**20%, Wednesday, October 25, in class.**Midterm Exam 2:**20%, Monday, November 20, in class.**Final Exam:**35%, Wednesday, December 13, 4:00 - 6:00pm.

There will be no make-up for the quizzes or exams for any reason. A missed midterm exam counts as zero points, with the following exception. If you miss a midterm exam due to a documented medical or family emergency, the exam's weight will be added to the weight of the final exam.

#### Friday, September 29

Permutations and combinations (Sections 1.1-1.4 just before binomial theorem).Homework 1 (due October 5): 1, 3, 4, 7, 8, 9, 13, 15, 16, 17, 18, 20a, 21, 22.#### Monday, October 2

The TA will lead this class, will discuss examples. Try as much homework problems as you can before this class. I (R.V.) will not hold office hours this Monday, but the TA will (2:00 - 3:00pm in 532 Rowland Hall).#### Wednesday, October 4

Combinations continued, multinomial coefficients (Sections 1.1-1.5).Homework 2 (due October 12): From Chapter 1: 23, 24, 27, Theoretical Exercises 5, 13. From Chapter 2: 1, 2, 3, 5, 6, 7.#### Friday, October 6

Number of integer solutions (1.6). Sample space and events. Operations on events (2.1-2.2).#### Monday, October 9

Axioms of probability. Inclusion-Exclusion Principle (2.4 up to Example 4a).#### Wednesday, October 11

Inclusion-Exclusion Principle continued. Sample spaces having equally likely outcomes (2.5 begins).#### Friday, October 13

Generalized Inclusion-Exclusion Principle (Proposition 4.4). The Matching Problem (Example 5m).Homework 3 (due October 19) from Chapter 2: 8, 9, 10, 12, 14, 17, 21, 25, 28, 29(a), 32, 37, 39, 41.#### Monday, October 16

Conditional probabilities. The Law of Total Probability (3.1-3.2).#### Wednesday, October 18

The Best Prize Problem (Chapter 7, Example 5k). Bayes Formula (3.3).#### Friday, October 20

Bayes Formula cont. Prior and posterior probabilities (Bayesian statistics). Bayesian spam filtering (Bayesian machine learning). Three Prisoners Problem.Homework 4 (due October 26) from Chapter 3: 1, 2, 4, 7, 12, 15, 16, 19, 20, 21, 23, 26, 33, 37, 51.#### Monday, October 23

Independent events (3.4). Computing probabilities by conditioning. Simple random walk (Example 4m).#### Wednesday, October 25

Midterm Exam 1, solutions.#### Friday, October 27

Independence cont. Finding your birthmate problem. Random variables (4.1). Discrete random variables. Probability mass function (4.2).Homework 5 (due November 2) from Chapter 3: 55, 57, 58, 62, 64, 66, 73, 81, 91; from Chapter 4: 1, 4, 5, 6, 14.#### Monday, October 30

Cumulative distribution function (cdf).#### Wednesday, November 1

Expected value (4.3). Examples: lottery; group testing. Expected value of a function of a random variable (4.4).#### Friday, November 3

Variance (4.5). The matching problem (expectation and variance). Analysis of Quicksort (Chapter 7, Example 2m).Homework 6 (due November 9) from Chapter 4: 17, 18, 19, 20, 21, 22(a), 23, 26, 30, 35, 36, 37, 38.#### Monday, November 6

Bernoulli and binomial distributions (4.6).#### Wednesday, November 8

Poisson distribution. Poisson approximation of the Binomial distribution (4.7). People vs. Collins.Homework 7 (due November 16) from Chapter 4: 39, 40, 41, 42, 43, 45, 49, 51, 52, 53, 55, 56 (use Poisson approximation), 57, 60.#### Monday, November 13

Computing expectations by conditioning: law ot total expectation (7.5). Geometric distribution (4.8.1). Coupon collector's problem (Ch.7 Ex. 2i).#### Wednesday, November 15

Negative binomial (4.8.2), the problem of points, Banach match problem. Hypergeometric distribution (4.8.3).#### Friday, November 17

Continuous distributions, pdf (5.1). Uniform distribution (5.3).#### Monday, November 20

Midterm Exam 2, solutions.The exam covers the material that we covered in class during October 23 (Section 3.4) through November 8 (Section 4.7).#### Wednesday, November 22

Transformations of random variables (5.7). Benford's law.Homework 8 (due November 30) from Chapter 7: 6, 7, 8, 11, 33, 53, 58; from Chapter 5: 1, 2, 4, 11, 13, 37, 40.#### Monday, November 27

Expectation and variance of continuous distributions (5.2)#### Wednesday, November 29

Normal distribution (5.4).#### Friday, December 1

Normal distribution cont. Normal approximation to binomial distribution (5.4.1).Homework 9 (due December 7) from Chapter 5: 6, 7, 14, 15, 16, 17, 18, 19, 20, 22, 23, 25, 26, 31(a), 38.#### Monday, November 4

Normal approximation cont. (5.4.1).#### Wednesday, November 6

Exponential distribution (5.5).Homework 10 (will not be collected) from Chapter 5: 32, 33, 34, 39.#### Friday, December 8

Review.#### Wednesday, December 13, 4:00-6:00 pm

Final Exam.

**Course webpage (this page):** https://www.math.uci.edu/~rvershyn/teaching/2017-18/130A/130A.html

**Canvas webpage (grades & chat room):** https://canvas.eee.uci.edu/courses/6640