| Monday | Wednesday | Friday | Homework | |
| Week 1 |
1/13. Syllabus. Logistics. Beginning basic principles of counting (combinatorics). Required reading: Sections 1.1-1.2 of Ross. Gambler's ruin Mathematica notebook(just for fun) |
1/15. Permutations and combinations. Required reading: Sections 1.3-1.4 of Ross. |
1/17. Multinomial coefficients. Required reading: Section 1.5 of Ross. |
Homework 1 consists of 6 problems from the end of Chapter 1 of Ross.
Due: Friday, 1/24 at the beginning of class. |
| Week 2 |
1/20 NO CLASS. MLK Day. |
1/22. Sample spaces and events (set theory). Required reading: 2.1, 2.2 |
1/24. Axioms of probability, and some simple consequences. Required reading: 2.3, 2.4 |
Homework 2 consists of 6 problems from the end of Chapter 2 of Ross.
Due: Friday, 1/31 at the beginning of class. |
| Week 3 |
1/27. Samples spaces having equally likely outcomes (aka uniform probability measure on a finite set). Lots of examples (including birthday "paradox"). Required reading: 2.5, 2.7 Last day to drop without a W |
1/29. More examples of uniform probability measure on a finite set (including matching problem) |
1/31. Conditional probability. Required reading: 3.1, 3.2 |
Homework 3 consists of 4 questions from the end of Chapter 2 of Ross, and 2 from the end of Chapter 3 .
Due: Friday, 2/7 at the beginning of class. |
| Week 4 |
2/3. Matching problem & multiplication rule for conditional probabilities. More computational tricks w/ conditional probabilities. Required reading: 3.3 No slides today. |
2/5. Law of Total Probability. Bayes's theorem. Required reading: continuing in 3.3 |
2/7. Odds. Independent events. Required reading: 3.4 |
Homework 4 consists of 6 problems from the end of Chapter 3 of Ross.
Due: Friday, 2/14 at the beginning of class. |
| Week 5 |
2/10. More examples from 3.4. No slides today. |
2/12. Conditional probability P(-|F) as a probability measure. Laplace's rule of succession. Required reading: 3.5 |
2/14 MT1 review. |
No homework due to MT1. |
| Week 6 |
2/17 MIDTERM 1. In-class at the usual time. MT1 covers everything up through this day. |
2/19. Real-valued random variables. Cumulative distribution functions. Discrete random variables. Probability mass functions Required reading: 4.1, 4.2 No draft problem due to MT1. |
2/21. More examples of discrete random variables, PMFs and CDFs. Required reading: finishing 4.1, 4.2 No slides today. |
Homework 5 consists of 5 questions from the end of Chapter 4 of Ross.
Due: Friday, 2/28 at the beginning of class. |
| Week 7 |
2/24. Expected value (aka expectation or mean) Required reading: 4.3 |
2/26. Expected value of a function of a random variable. Required reading: 4.4 |
2/28. Friendship paradox. Variance. Required reading: 4.5 |
Homework 6 consists of 6 questions from the end of Chapter 4 of Ross.
Due: Friday, 3/7 at the beginning of class. |
| Week 8 |
3/3. Bernoulli and binomial random variables. Required reading: 4.6 |
3/5. Poisson random variables. Required reading: 4.7 |
3/7. Poisson processes. Linearity of expectation. Required reading: 4.9 |
Homework 7 consists of 6 questions from the end of Chapter 4 of Ross.
Due: Friday, 3/14 at the beginning of class. |
| Week 9 |
3/10. Continuous random variables, and their PDFs, CDFs, expectation and variance. Uniform random variables on a bounded interval. Required reading: 5.1, 5.2, 5.3 |
3/12. Normal random variables. Required reading: 5.4 |
3/14. Normal approximation to binomial random variables. Required reading: more on 5.4 |
Homework 8 consists of 6 questions from the end of Chapter 5 of Ross.
Due: Friday, 3/28 at the beginning of class. |
| SPRING BREAK |
3/17 |
3/19 |
3/21 |
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| Week 10 |
3/24. Exponential random variables. Hazard rate functions. Memorylessness. Required reading: 5.5 |
3/26. More on memorylessness. Geometric random variables. Required reading: 4.8.1 |
3/28. PDFs of functions of random variables. Required reading: 5.7 |
Homework 9 consists of 6 questions from the end of Chapter 5 of Ross.
Due: Friday, 4/4 at the beginning of class. |
| Week 11 |
3/31. Joint distribution functions. Required reading: 6.1 |
4/2. Independent random variables. Required reading: 6.2 |
4/4 MT2 review Practice Exam Solutions(not available until Friday) |
No homework due to MT2. |
| Week 12 |
4/7 MIDTERM 2. In-class at the usual time. MT2 covers everything up through this day, but will especially focus on the material since MT1. |
4/9 INTERLUDE: Law of Large Numbers and Central Limit Theorem. You should read as much of 8.1-8.4 as you can. |
4/11. Sums of independent random variables. Required reading: 6.3 |
Homework 10 consists of 6 questions from the end of Chapter 6 of Ross.
Due: Friday, 4/18 at the beginning of class. |
| Week 13 |
4/14. Conditional distributions (discrete case). Required reading: 6.4 |
4/16. Conditional distributions (continuous case). Required reading: 6.5 |
4/18. Expectation of sums of random variables. DROP DEADLINE (W) Required reading: 7.1, 7.2 |
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| Week 14 |
4/21 Required reading: 7.3 |
4/23 Required reading: 7.4 |
4/25 Required reading: 7.7 |
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| Week 15 |
4/28 Required reading: selections from 8.1-8.4 |
4/30 FINAL REVIEW. |
5/2 Professor Samperton be out of town. Will hold virtual lecture/discussion about quantum mechanics. |
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| FINAL EXAM: Thursday, 5/8, 08:00am - 10:00am in LILY G126 |
