Instructor: Vahan Huroyan

Email: vahanhuroyan (at) math (dot) arizona (dot) edu

Section Time: T TH 11:00 - 12:15

Section Room: Communication, Rm 113

Office Hours: Physics-Atmospheric Sciences (PAS) 514: W TH 2:00-3:00; Mathematics 220: T 2:00-3:00

Course Syllabus: [

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Textbook:

Introduction to Probability, by David F. Anderson, Benedek Valkó, Timo Seppäläinen.

### Announcements:

Lecture 1, Aug. 27: Sample Spaces and Probabilities. (Section 1.1) Lecture 2, Aug. 29: Random Sampling. Infinitely many outcomes. (Sections 1.2 and 1.3) Lecture 3, Sep. 3: Consequences of the Rules of Probability. (Section 1.4) Lecture 4, Sep. 5: Random Variables: a first look. Conditional Probability. (Sections 1.5 and 2.1) Lecture 5, Sep. 10: Bayes' Formula. (Section 2.2) Lecture 6, Sep. 12: Independence. (Section 2.3) Lecture 7, Sep. 17: Independent trials. (Section 2.4) Lecture 8, Sep. 19: Further topics for sampling and independence. (Section 2.5) Lecture 9, Sep. 24: Conditional independence, Probability distributions of random variables. (Sections 2.5, 3.1) Lecture 10, Sep. 26: Probability distributions of random variables. (Section 3.1) Lecture 11, Oct. 1: Cumulative distribution function. (Section 3.2) Lecture 12, Oct. 3: Expectation. (Section 3.3) Lecture 13, Oct. 8: Review. Lecture 14, Oct. 10: ([Midterm 1]). Lecture 15, Oct. 15: Expectation. (Section 3.3) Lecture 16, Oct. 17: Variance. (Section 3.4) Lecture 17, Oct. 22: Gaussian distribution. (Section 3.5) Lecture 18, Oct. 24: Normal approximation, Central Limit Theorem. (Section 4.1) Lecture 19, Oct. 29: Law of large numbers, Applications of the normal approximation. (Sections 4.2, 4.3) Lecture 20, Oct. 31: Poisson approximation. (Section 4.4) Lecture 21, Nov. 5: Exponential distribution. (Section 4.5) Lecture 22, Nov. 7: Moment generating function. (Section 5.1) Lecture 23, Nov. 12: Distribution of a function of a random variable. (Section 5.2) Lecture 24, Nov. 14: Joint distribution of randmom variables. (Section 6.1) Lecture 25, Nov. 19: Review. Lecture 26, Nov. 21: Midterm 2. Lecture 27, Nov. 26: Jointly continuous random variables. (Section 6.2) Lecture 28, Dec. 3: Joint distribitions and independence. (Section 6.3) Lecture 29, Dec. 5: Sums of independent randome variavles, Exchangeable random variables. (Sections 7.1, 7.2) Lecture 30, Dec. 10: Linearity of expectation. (Sections 8.1)

### Homework:

HW 1: posted 09/06, due 09/17 ---- 1.2, 1.5, 1.8, 1.13, 1.17, 1.19, 1.33, 1.40. HW 2: posted 09/19, due 10/01 ---- 2.4, 2.7, 2.10, 2.14, 2.18, 2.22, 2.25, 2.31, 2.33, 2.54. HW 3: posted 10/03, due 10/17 ---- 2.24, 2.26, 3.3, 3.4, 3.5, 3.7, 3.8, 3.9, 3.10, 3.12 HW 4: posted 10/23, due 11/5 ---- 3.15, 3.18, 3.20, 3.22, 3.32, 3.37, 3.40, 3.56, 3.58, 3.67, 3.71 HW 5: posted 11/07, due 11/19 ---- 4.4, 4.5, 4.17, 4.20, 4.23, 4.28, 4.33, 4.35, 4.41, 4.47, 4.48 HW 6: posted 11/26, due 12/10 ---- 5.2, 5.3, 5.7, 5.12, 5.16, 5.19, 5.25, 5.35, 6.1, 6.2, 6.7, 6.11, 6.22, 6.29, 6.30 HW 7: posted 12/10, (no need to submit the homework, these are just suggested problems) ---- 6.35, 6.36, 7.2, 7.4, 7.6, 7.8, 7.16, 7.20, 7.24, 7.27, 8.1, 8.3, 8.20, 8.21