Offers selected topics in probability such as sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk, conditioning and martingales, Markov chains and Brownian motion.
Ongoing course
Time: MWF 11:30 AM – 12:20 PM
Location: CLRE 208
Office hours: See details here
Grading
Homework: 30% – Weekly homework (you must turn them in)
Midterm: 30% – TBA
Final : 40% – TBA
Homework sets
All problems refer to our textbook.
Textbook
Some books that may be useful in this course
Course notes
Constructing independent random variables – MATH 6534
How to construct sequence of independent r.v?
Joint distributions and expectations of independent r.v.s – MATH 6534
Joint distributions and nice property of expected value of product of independent random variables.
Sufficient conditions for independence – MATH 6534
Proving a nice tool to show independence!
Variance and Tail bounds – MATH 6534
Why should we care about CDF? Given a distribution function F, does there exist a random variable whose CDF is F?
Expected Value – MATH 6534
Why should we care about CDF? Given a distribution function F, does there exist a random variable whose CDF is F?
Random Variables II – MATH 6534
Why should we care about CDF? Given a distribution function F, does there exist a random variable whose CDF is F?
Probability and Measure Theory – MATH 6534
The right definition for probability, important concepts from measure theory
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