STA 4321: Introduction to Probability
Lecture. 11:45am - 12:35pm on Monday, Wednesday, and Friday [Zoom link]
Instructor. Aaron J. Molstad (amolstad@ufl.edu)
Office hours. Mon (10:15 - 11:15am), Thurs (5:30 - 6:30pm) on Zoom [Zoom link]
Teaching assistant. Ruoyang Zhang (njiandan@ufl.edu)
Office hours. Tuesday from 10:00am - 12:00pm on Zoom [Zoom link]
Syllabus. [pdf]
Note that you must be logged into your UFL eLearning account to access course materials.
| Lecture | Topics (suggested readings) | |||
| 1 (1/11) | Syllabus, basic set theory, sample spaces (2.3 - 2.4) [pdf] | |||
| 2 (1/13) | Set theory, sample spaces, axioms of probability (2.1 - 2.5) [pdf][lecture][notes] | |||
| 3 (1/15) | Axioms of probability, counting rules, permutations (2.6) [pdf][lecture][notes] | |||
| 4 (1/20) | Permuations, combinations, examples [pdf][lecture][notes] |
Homework 1 (Due: 5:00pm on Wednesday, January 27th) [pdf][submit][solutions]
| 5 (1/22) | Conditional probability, independence (2.7 - 2.8) [pdf][lecture][correction] | |||
| 6 (1/25) | Inclusion-exclusion, law of total probability (2.8, 2.10) [pdf][lecture] | |||
| 7 (1/27) | Bayes rule, “Monty Hall” problem [pdf][lecture] |
Homework 2 (Due: 5:00pm on Wednesday, February 3rd) [pdf][submit][solution]
| 8 (1/29) | Discrete random variables, probability mass function (2.11, 3.1, 3.2) [pdf][lecture] | |||
| 9 (2/1) | Distribution function, expected value (3.3) [pdf][lecture] | |||
| 10 (2/3) | Variance, Chebyshev’s theorem (3.3) [pdf][lecture] |
Homework 3 (Due: 5:00pm on Wednesday, February 10rd) [pdf][submit][solutions]
| 11 (2/5) | Bernoulli and Binomial random variables [pdf][lecture] |
Exam 1 (7:00pm on Wednesday, February 17th) [practice][practice solutions][notes][solutions]
Exam 1 Correction (Due: 5:00pm on Sunday, March 7th) [pdf][submission]
| 12 (2/8) | Geometric distribution (3.5) [pdf][lecture] | |||
| 13 (2/10) | Geometric and negative binomial distributions (3.5, 3.6)[pdf][lecture] | |||
| 14 (2/12) | Examples, Poisson distribution (3.8) [pdf][lecture] | |||
| 15 (2/15) | Example, Hypergeometric distribution (3.8, 3.7) [pdf][lecture] | |||
| 16 (2/17) | Exam 1 review [lecture] |
Homework 4 (Due: 11:45am on Friday, March 5rd) [pdf][submission][solutions]
| 17 (2/22) | Continuous random variables, densities (4.2) [pdf][lecture] | |||
| 18 (2/24) | Properties of densities, examples (4.2) [pdf][lecture] | |||
| 19 (2/26) | Expected values and variances (4.3) [pdf][lecture] | |||
| 20 (3/1) | Uniform random variables (4.4) [pdf][lecture] | |||
| 21 (3/3) | Uniform distribution, exponential distribution (4.4, 4.6) [pdf][lecture] |
Homework 5 (Due: 5:00pm on Thursday, March 11th) [pdf][submission][solutions]
| 22 (3/5) | Exponential distribution, Gamma distribution (4.6) [pdf][lecture] | |||
| 23 (3/8) | Gamma distribution, Normal distribution (4.5, 4.6) [pdf][lecture] | |||
| 24 (3/10) | Normal distribution, beta distribution (4.5, 4.7) [pdf][lecture] | |||
| 25 (3/12) | Beta distribution [pdf][lecture] | |||
| 26 (3/15) | Moment generating functions (6.5) [pdf][lecture] | |||
| 00 (3/22) | Exam 2 Review [pdf][lecture] |
Homework 6 (Due: 5:00pm on Friday, March 19th) [pdf][submission][solutions]
Exam 2 (7:00 - 9:00pm on Thursday, March 25th) [practice][lectures][curve][solutions]
| 27 (3/17) | MGFs continued, Joint distributions (6.5,5.2,5.3) [pdf][lecture] | |||
| 28 (3/19) | Joint distributions of continuous random variables (5.3) [pdf][lecture] | |||
| 29 (3/29) | Joint distributions, independence (5.4) [pdf][lecture] |
Homework 7 (Due: 5:00pm on Monday, April 5th) [pdf][submission][solutions]
| 30 (3/31) | Probabilities with two random variables (5.3) [pdf][lecture] | |||
| 31 (4/2) | Expectations, covariance and correlation (5.8, 5.7) [pdf][lecture] | |||
| 32 (4/5) | Covariance and correlation, examples (5.7) [pdf][lecture] | |||
| 33 (4/7) | Conditional expectations (5.11) [pdf][lecture] | |||
| 34 (4/9) | Conditional expectations continued (5.11) [pdf][lecture] |
Homework 8 (Due: 5:00pm on Monday, April 12th) [pdf][submission][solutions]
| 35 (4/12) | Functions of random variables (6.2, 6.3) [pdf]][lecture] | |||
| 36 (4/14) | Method of transformations (6.4) [pdf][lecture] | |||
| 00 (4/19) | Exam 3 Review #1 [lecture] |
Homework 9 (Due: 5:00pm on Monday, April 19th) [pdf][submission][solutions]
Exam 3 (7:00 - 9:00pm, on Wednesday, April 21) [practice][practice solutions][lectures]