Probability and Statistics
Spring 2020 - MI2026
Course Description
MI2026: Probability and Statistics. This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, hypothesis testing, confidence intervals, and linear regression.
-- Announcements --
-
The first class is Wednesday Mar 4.
-- Course info --
-
Instructor: Tran Manh Tuan, tuan.tranmanh@hust.edu.vn
-
Lecture: Wednesday, 7:00-9:15
-
Discussion Session: Thursday, 7:00-8:20
-
Textbook: There is no required text for the first part of the course; instead, lecture notes will be made available on this site. For the second part, I will follow the textbook ''A course in probability and statistics'' by Nguyen Van Ho.
-
Prerequisites: Calculus I (MI1016) and Calculus II (MI1026).
-
Homework: The homework assignments will be posted here every Friday (at midnight).
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Homework Submission deadline
Exercise Sheet 3 01.04.2020
Exercise Sheet 5 (Ex. 3 has been updated) 15.04.2020
Exercise Sheet 6 22.04.2020
Exercise Sheet 7 29.04.2020
Exercise Sheet 8 06.05.2020
Exercise Sheet 9 13.05.2020
Exercise Sheet 10 27.05.2020
Exercise Sheet 11 03.06.2020
Exercise Sheet 12 10.06.2020
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Course Progress
Week
1
2
3
4
5
6
7
8
9
10
11
12
Topics
Descriptive statistics
Basic notions of Probability Theory: sample space, events, axioms of probabilities. Counting outcomes: permutations, combinations.
Conditional probability: definition, the law of total probability, chain rule, Bayes' theorem.
Independent events.
Discrete and continuous random variables: definition, cumulative distribution function, expectation, variance.
Random vector; Joint distributions: joint probability mass function, joint probability density function, joint cumulative distribution function.
Independent random variables; Covariance and correlation matrices; Conditional expectation.
Several discrete random variables: uniform, hypergeometric, Bernoulli, and Poisson distributions.
Several continuous random variables: uniform, exponential, normal, chi-squared, student distributions; CLT.
Point estimation: estimating the population mean, the population variance, a proportion.
Confidence interval for: the mean, the proportion, the variance.
Testing statistical hypothesis: population mean, population variance, the proportion p; difference between two normal means; two proportions in two populations; two normal variances.
Regression Analysis: linear regression model; estimating model parameters; error and estimating variance
Lectures
Chapter 8 in Nguyen Van Ho's textbook.
Chapter 9 in the textbook.
Chapter 10 in the textbook.
Chap 11 in the textbook.