Course Information

Instructor: Daesung Kim (daesungk (at) illinois.edu)
Time: MWF 9-9:50am (Section B13), MWF 10-10:50am (Section C13)
Zoom Office Hour: Tue and Fri at 11am - 12pm.
Textbook: Sheldon Ross, A First Course in Probability, 9th Edition, ISBN: 9780321794772.
Supplementary textbook: Introduction to Probability, Blitzstein and Hwang
Syllabus, Course overview
Moodle: https://learn.illinois.edu/course/view.php?id=57178
Campuswire: https://campuswire.com/p/G656D198C (Code is available on the Moodle course page.)
PrairieLearn: https://prairielearn.engr.illinois.edu/pl
Lecture videos are available at Mediaspace.
Prerequisite: Math 241 or the equivalent. We will use important topics from calculus, such as infinite series with positive terms (most calculations involve the geometric series and series derived from it), improper integrals and double integrals (change of variables formula, manipulating Gaussian integrals).

Grading policy

HW: 20% (weekly, the lowest one HW will be dropped.)
Online quizzes: 20% (biweekly, in class, the loewst one quiz will be dropped.)
Midterms: 15% and 20% (Mar 10 and Apr 21, in class, the lower exam score will be 15% and the other 20%.)
Final: 25%

Tentative Schedule

Note	Date	Topic	Assignments
W1	Jan 25	Basic Combinatorics I (Sec 1.1-3)
	Jan 27	Basic Combinatorics II (Sec 1.4-6)
	Jan 29	Basic Combinatorics III (Sec 1.4-6)
W2	Feb 1	Axioms of Probability I (Sec 2.2-3)
	Feb 3	Axioms of Probability II (Sec 2.4)	Quiz 1
	Feb 5	Sample spaces having equally likely (Sec 2.5)	HW 1
W3	Feb 8	Conditional Probabilities (Sec 3.2)
	Feb 10	Bayes's Formula (Sec 3.3)
	Feb 12	Independent Events (Sec 3.4)	HW 2
W4	Feb 15	Random Variables (Sec 4.1-2, 10)	Quiz 2
	Feb 17	No class
	Feb 19	Expectation (Sec 4.3, 4, 6)	HW 3
W5	Feb 22	Variance (Sec 4.5)
	Feb 24	Bernoulli and Binomial RVs (Sec 4.6)
	Feb 26	Poisson RVs (Sec 4.7)	HW 4
W6	Mar 1	Other discrete rvs (sec 4.8)
	Mar 3	Other discrete rvs (sec 4.8)	quiz 3
	Mar 5	Intro to continuous random variables (sec 5.1)	hw 5
W7	Mar 8	Review
	Mar 10	Midterm 1
	Mar 12	Expectation and variance of continuous rvs (sec 5.2)
W8	Mar 15	The uniform random variable (sec 5.3)
	Mar 17	Normal random variables (sec 5.4-7)	quiz 4
	Mar 19	Exponential random variables (sec 5.4-7)	hw 6
W9	Mar 22	Other random variables (sec 5.4-7)
	Mar 24	No class
	Mar 26	Joint distribution functions i (sec 6.1)	hw 7
W10	Mar 29	Joint distribution functions ii (sec 6.1)
	Mar 31	Independent random variables (sec 6.2)	quiz 5
	Apr 2	Sums of independent random variables (sec 6.3)
W11	Apr 5	Conditional distribution (sec 6.4-5)	hw 8
	Apr 7	Joint distribution of functions of rvs (sec 6.7)
	Apr 9	Expectation of functions of rvs (sec 7.2)
W12	Apr 12	The number of events that occur (sec 7.3)	hw 9
	Apr 14	Covariance (sec 7.4)	quiz 6
	Apr 16	Conditional expectation (sec 7.5)
W13	Apr 19	Review	hw 10
	Apr 21	Midterm 2
	Apr 23	Moment generating functions (sec 7.7)
W14	Apr 26	Markov's and chebyshev's inequalities (sec 8.2)
	Apr 28	Other inequalities (sec 8.5)	quiz 7
	Apr 30	The law of large numbers (sec 8.2, 4)
W15	May 3	Central limit theorem (sec 8.3)
	May 5	Review	hw 11
Final week	May 7-12	Final take-home exam
	May 13-14	Final prairielearn exam