Math 130A: Probability and Stochastic Processes, Spring 2017

Course code: 44860


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 pdf
Lecture 2 Combinations (choose function) pdf
Lecture 3 Binomial Theorem, Multinomial Coefficients pdf
Lecture 4 # of ways n_1 + … + n_r = n pdf
Lecture 5 Axioms of probability pdf
Lecture 6 Subset stuff, consequences of axioms pdf
Lecture 7 More consequences of axioms, cool examples pdf
Lecture 8 Example problems, degree of belief (lec 7 notes)
Lecture 9 Harder examples with inclusion-exclusion principle pdf
Lecture 10 Conditional probability, examples pdf
Lecture 11 Conditional probability, Bayes Theorem pdf
Lecture 12 Bayes Theorem examples, medical tests, prior knowledge pdf
Lecture 13 Bayes Theorem examples, Independence pdf
Lecture 14 Independence, examples, Watashi wa scientesto pdf
Lecture 15 Probability axioms for conditional probability, properties, examples pdf
Lecture 17 Discrete random variables, probability mass function pdf
Lecture 18 Expectation pdf
Lecture 19 Conditional probability review, more expectation pdf
Lecture 20 More expectation, Bernouilli and binomial random variables pdf
Lecture 21 Binomial random variable examples, elections pdf
Lecture 22 Poisson random variable, examples pdf
Lecture 23 E(Poisson), Var(Poisson), expected number of attempts to get 10 tosses in a row pdf
Lecture 24 Geometric, Negative Binomial, Hypergeometric random variables, examples pdf
Lecture 25 Continuous random variables, PDF, CDF pdf
Lecture 26 Continuous random variables, expectation pdf
Lecture 27 Optimizing expected gain, Normal random variable pdf
Lecture 28 Normal random variable, examples pdf
Lecture 29 Exponential, gamma and Beta random variables pdf

###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