Time: Mondays and Wednesdays 12:30-1:45 pm
Room: Warren Weaver Hall 512
Instructor: Professor Nina Holden, firstname.lastname@nyu.edu
Office hours: Mondays 1:45-3:00 pm, WWH 813
Recitations by TA Xiaoou Cheng: Fridays 3:30-4:45 pm
Course description: An introduction to the mathematical treatment of random phenomena occurring in the natural, physical, and social sciences. Axioms of mathematical probability, combinatorial analysis, binomial distribution, Poisson and normal approximation, random variables and probability distributions, generating functions, Markov chains applications.
Textbook: Ross, A First Course in Probability (8th, 9th or 10th edition)
Grading and problem sets: Weekly problem sets (10%, two lowest homeworks dropped), two midterm exams (each 25%) and final exam (40%).
Tentative plan for lectures:
W 1/21: Counting, permutations, combinations. Ross 1.1-1.4
M 1/26: Multinomial coefficients, sample spaces. Ross 1.5, 2.1-2.2
W 1/28: Axioms of probability, some propositions. Ross 2.3-2.4
M 2/2: Sample spaces with equally likely outcomes, probability as belief. Ross 2.5, 2.7
W 2/4: Conditional probability, Bayes' rule. Ross 3.1-3.3
M 2/9: Independent events. Ross 3.4
W 2/11: Conditional probably, again. Ross 3.5
T 2/17: Discrete random variables, expected value. Ross 4.1-4.3
W 2/18: Expectations of functions of a RV; variance. Ross 4.4-4.5
M 2/23: Bernoulli and binomial random variables. Ross 4.6
W 2/25: Exam 1 (TBC)
M 3/2: Poisson random variables. Ross 4.7
W 3/4: Other discrete random variables, expectations of sums; Properties of the CDF. Ross 4.8-4.10
M 3/9: Continuous random variables. Ross 5.1-5.2
W 3/11: Uniform and normal random variables. Ross 5.3-5.4
M 3/23: Normal approximation to the binomial distribution Exponential, Gamma, and Cauchy distributions. Ross 5.4.1, 5.5-5.6
W 3/25: Functions of continuous random variables; joint distributions. Ross 5.7, 6.1
M 3/30: Distribution of sums of independent random variables. Ross 6.2-6.3
W 4/1: Exam 2 (TBC)
M 4/6: Conditional distributions. Ross 6.4-6.5
W 4/8: Order statistics; functions of several random variables. Ross 6.6-6.7
M 4/13: Expectations of sums, covariance, correlation. Ross 7.1-7.2, 7.4
W 4/15: Conditional expectation and prediction. Ross 7.5-7.6
M 4/20: Moment generating functions; properties of normal variates. Ross 7.7-7.8
W 4/22: Central Limit Theorem. Ross 8.1-8.3
M 4/27: Strong Law of Large Numbers, more inequalities. Ross 8.4-8.5
W 4/29: Poisson processes. Ross 9.1
M 5/4: TBD
TBD: Final Exam