Math 130A: Probability and Stochastic Processes, Spring 2017
Welcome. Uncertainty can come from having limited information about the world (e.g. in statistics, data science) as well as nature itself (quantum mechanics). Even under uncertain conditions, deductions with various degrees of certainty can be made. Probability theory is the study of working mathematically in order to make such deductions and is one of the formalisms underlying statistics, data science and machine learning, physics, as well as a lot of interesting mathematics. In this course, you will learn the basics of probability. You will learn to prove and apply some basic theorems as well as work with combinatorial and continuous abstract and real world examples.
Here is the suggested syllabus.
Text: A First Course in Probability, S. Ross
Assessment consists of:
Weekly homeworks (30%)
Discussion-time problem sessions (10%, graded based on completion, one score dropped)
Midterm (May 8, 20%)
Final exam (comprehensive) (Jun 12, 40%)
Homeworks
It is crucial for your success in this course that you do homework problems, which will be posted here weekly.
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Lectures
The notes here are my own notes for the lectures. I am sharing them with you in case they are useful.
| Lecture 1 | Counting, permutations | |
| Lecture 2 | Combinations (choose function) | |
| Lecture 3 | Binomial Theorem, Multinomial Coefficients | |
| Lecture 4 | # of ways n_1 + … + n_r = n | |
| Lecture 5 | Axioms of probability | |
| Lecture 6 | Subset stuff, consequences of axioms | |
| Lecture 7 | More consequences of axioms, cool examples | |
| Lecture 8 | Example problems, degree of belief | (lec 7 notes) |
| Lecture 9 | Harder examples with inclusion-exclusion principle | |
| Lecture 10 | Conditional probability, examples | |
| Lecture 11 | Conditional probability, Bayes Theorem | |
| Lecture 12 | Bayes Theorem examples, medical tests, prior knowledge | |
| Lecture 13 | Bayes Theorem examples, Independence | |
| Lecture 14 | Independence, examples, Watashi wa scientesto | |
| Lecture 15 | Probability axioms for conditional probability, properties, examples | |
| Lecture 17 | Discrete random variables, probability mass function | |
| Lecture 18 | Expectation | |
| Lecture 19 | Conditional probability review, more expectation | |
| Lecture 20 | More expectation, Bernouilli and binomial random variables | |
| Lecture 21 | Binomial random variable examples, elections | |
| Lecture 22 | Poisson random variable, examples | |
| Lecture 23 | E(Poisson), Var(Poisson), expected number of attempts to get 10 tosses in a row | |
| Lecture 24 | Geometric, Negative Binomial, Hypergeometric random variables, examples | |
| Lecture 25 | Continuous random variables, PDF, CDF | |
| Lecture 26 | Continuous random variables, expectation | |
| Lecture 27 | Optimizing expected gain, Normal random variable | |
| Lecture 28 | Normal random variable, examples | |
| Lecture 29 | Exponential, gamma and Beta random variables |
###Office Hours
- Office Location: 510P Rowland Hall (5th floor, turn right when you exit the elevator, then left, 510 is a door on the right past the tutoring center)
- Office hours: Mondays 4-5 pm, Wednesdays 11 am - 12 pm, Fridays 4-5 pm
###Contact Information
- Umut Isik
- Email: misik@uci.edu
- Phone: (949) 824-3153
###Your TA
- Huiwen Wu
- Office hours: Mondays 9-10 am, Wednesdays 3-4 pm
- Office: 533 Rowland Hall
###Campus Resources