Developing Timetable for MATH 3100, Spring 2020 - ShermanIntroduction to Probability |
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Date | Main lecture topics | Relevant reading | Homework due (posted on Collab) |
1/14 | Hello. Syllabus. Questionnaire. Mathematical setup for a probability experiment: sample space, events, probability measure and its properties. Examples. Cartesian products. Sampling with and without replacement. Classwork. | 1.1-2 | |
1/16 | Review of last lecture and some parts of classwork. How to count some things. Some infinite sample spaces: flipping until a head, and choosing a point uniformly at random. Clickers. | 1.2-3 | |
1/21 | Counting and decision trees. Why points have zero probability when choosing uniformly at random from an interval or 2D region. Probabilities and parities. Some rules and Venn diagrams. Clickers throughout. | 1.3-4 | |
1/23 | Inclusion-exclusion. Law of Large Numbers as the meaning of the probability of an event. Basic terminology of random variables, examples, and classwork. | 1.5 | HW 1 |
1/28 | Review of some classwork from last time: inclusion-exclusion and a pmf. Conditional probability: definition, multiplicative rule, decision trees and the law of total probability. Some practice problems, leading to Bayes' formula. | 2.1-2 | |
1/30 | Review of previous lecture, with practice. Bayes' formula. Independence for events and r.v. Bernoulli and binomial r.v. | 2.2-4 | HW 2 |
2/4 | Geometric r.v. Probability density functions, properties and examples, including the uniform distribution. The Monty Hall problem. Clickers and classwork. | 2.4, 3.1 | |
2/6 | Clickers: the birthday problem, independence versus pairwise independence. Review of density functions. Cumulative distribution functions. Classwork. | 2.5: conditional independence and the birthday problem, 3.2 | HW 3 |
2/11 | Conditional independence. Expectations of discrete and continuous r.v., also expectations of functions of such. Expectations don't always exist. Computing cdfs and extracting pmfs, pdfs, and probabilities from them. Classwork. | 3.2-3 | |
2/13 | Examples: distance to the center of a dartboard, amount paid in the presence of a deductible, expectation of X ~ Bin(n,p). Classwork. | 3.2-3 | HW 4 |
2/18 | Another example: length of the longer piece of a broken stick. Terminology: moments, median, quantiles, variance, standard deviation. Revisiting a HW problem. Classwork. | 3.2-4 | |
2/19 | Midterm 1, 7-8:30 PM, Olsson 120 | ||
2/20 | Review of 3.2-3. Facts about variance. The standard normal: density, cdf, and properties. Other normal r.v. The Central Limit Theorem for binomial r.v. Classwork. | 3.4-5,4.1 | |
2/25 | Review of variance, standard normal, other normals, CLT. Normal approximation to the binomial, with examples and classwork. | 3.5,4.1 | |
2/27 | Law of Large Numbers for binomial r.v. Percentage of the sample within one or two standard deviations of the mean, for a normal r.v. Review of the normal approximation to the binomial, with a condition to check, the continuity correction, and a variation for random walks. Clickers. | 4.1-2 | HW 5 |
3/3 | LLN: meaning, proof. Confidence intervals. Poisson r.v. and the Law of Rare Events. Clickers. | 4.2-4 | |
3/5 | A HW problem. Proof of LRE. Using Poisson to estimate the number of occurrences of rare approximately independent events. Exponential r.v. and their use as approximate waiting times. Clickers. | 4.4-5 | HW 6 |
The course moved online during spring break. Course information is now kept exclusively on Collab. |