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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,

  • 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 1

Exercise Sheet 2

Exercise Sheet 3                                                      01.04.2020

Exercise Sheet 4                                                                   08.04.2020

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

Midterm Exam

Exercise Sheet 10                                                    27.05.2020

Exercise Sheet 11                                                                   03.06.2020


Exercise Sheet 12                                                                 10.06.2020                                                                                       


Course Progress
















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 


Lecture 2

Lecture 3


Lecture 4

Lecture 5 - part I

Lecture 5 - parts I+II

Lecture 6

Lecture 7

Chapter 8 in Nguyen Van Ho's textbook.

Chapter 9 in the textbook.

Chapter 10 in the textbook.

Chap 11 in the textbook. 

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