# TDAB01 Probability and Statistics

### Course information

#### Course literature

Baron, M.: Probability and Statistics for Computer Scientists. CRC Press. Ed. 3 or 2 (textbook)**Slides**

### Course structure

The course material is presented in**lectures**. Recommended exercises for self-study are listed. Selected exercises will be considered in detail in

**seminars**. In

**computer labs**practical solutions using R-programming will be discussed.

### Probability theory

**Lecture 1**: Probability

Ch. 1-2 in textbook | Slides

**Recommended exercises**: 2.1, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.11, 2.14, 2.16, 2.17, 2.32/2.33 | Facit

**Seminar 1**: 2.1, 2.4, 2.8, 2.16, 2.32/2.33 (2.32 in ed. 2 and 2.33 in ed. 3)

**Lecture 2**: Discrete Random Variables

Ch. 3.1-3.3 (not 3.3.8) in textbook | Slides

**Recommended exercises**: 3.1, 3.2, 3.4, 3.8, 3.9, 3.10, 3.11, 3.12, 3.13, 3.16, 3.19 | Facit

**Seminar 2**: 3.1, 3.2, 3.9, 3.10, 3.12, 3.19

**Lecture 3**: Families of Discrete Distributions

Ch. 3.4 in textbook | Slides

**Recommended exercises**: 3.5, 3.20, 3.21, 3.23, 3.24, 3.25, 3.27/3.28, 3.28/3.29, 3.29/3.30, 3.30/3.31, 3.31/3.32, 3.32/3.33, 3.35/3.36, 3.36/3.37, 3.37/3.38 | Facit

**Seminar 3**: 3.24, 3.27/3.28, 3.28/3.29, 3.32/3.33, 3.36/3.37

**R-code**: ManipDistributions.R

**Lecture 4**: Families of Continuous Distributions

Ch. 4 (not 4.3), p. 407 and 410 for ed. 2, or p. 422 and 424 for ed. 3, in textbook | Slides

**Recommended exercises**: 4.2, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.14, 4.16, 4.17, 4.18, 4.19, 4.29/4.31, 4.30/4.32, 4.32/4.34 | Facit

**Seminar 4**: 4.2, 4.7, 4.11 a), 4.14, 4.18, 4.30/4.32

**Additional material**: Normal distribution vs. t-distribution

**Lecture 5**: Central Limit Theorem, Simulations, Monte Carlo Methods

Ch. 4.3, 5.1, 5.2.1-5.2.3, 5.3.1-5.3.2 in textbook | Slides

**Recommended exercises**: 4.23, 4.24, 4.25, 4.26, 4.27, 4.28/4.30, 4.31/4.33, 5.1, 5.2, 5.6 | Facit

**Seminar 5**: 4.24, 4.25, 4.31/4.33, 5.1, 5.6

**Lecture 6**: Stochastic Processes

Ch. 6.1-6.3 in textbook | Slides

**Recommended exercises**: 6.1 (a,b,c), 6.3, 6.9, 6.12, 6.14, 6.17, 6.18, 6.19, 6.20, 6.21, 6.22, 6.23, 6.24 | Facit

**Seminar 6**: 6.1 (a,c), 6.9, 6.18, 6.22, 6.23

**R-code**: SimulateMarkovChain.R | SimulateBinomialProcess.R | SimulatePoissonProcess.R

### Statistics

**Lecture 7**: Introduction to Statistics

Ch. 8 (not 8.2.6, 8.3.2, 8.3.3) in textbook | Slides

**Recommended exercises**: 8.1 (b), 8.2 (a,b), 8.3, 8.4, 8.5, 8.6, 8.7 (a,b), 8.9 | Facit

**Seminar 7**: 8.4, 8.5, 8.6, 8.7 (a,b), 8.9

**R-code**: SS7GraferDemo.R

**Additional material**: Simple graphics in R | Introduction to more advanced graphics in R ggplot2

**Lecture 8**: Maximum Likelihood Estimator, Confidence Intervals

Ch. 9.1 (not 9.1.1), 9.2.1, 9.2.2, 9.3.1, 9.3.2, 9.3.4 in textbook | Slides

**Recommended exercises**: 9.1, 9.2, 9.3, 9.4 (Use only ML method for all problems) | Facit

**Seminar 8**: 9.1, 9.3 b)-d), 9.4 (Use only ML method for all problems)

**Additional material**: Interpreting Confidence Intervals

**Lecture 9**: Hypothesis Testing

Ch. 9.4.1-9.4.6, 9.4.8, 9.4.10, 9.5.1-9.5.3 in textbook | Slides

**Recommended exercises**: 9.7, 9.8, 9.9, 9.10, 9.12, 9.13, 9.16, 9.17 | Facit

**Seminar 9**: 9.7, 9.8, 9.9 a) and b), 9.10, 9.16 b)

**Additional material**: Understanding Hypothesis Testing

**Lecture 10**: Bayesian Inference

Ch. 10.4 in textbook | Slides

**Recommended exercises**: 10.31, 10.32, 10.33, 10.34, 10.35, 10.36, 10.37, 10.39, 10.40 | Facit

**Seminar 10**: 10.32, 10.33 a)-c), 10.34 a), 10.35 (in d) compare only estimators), 10.40 a)

**Additional material**: Bayesian methods | Illustration of exercise 10.32

**Lecture 11**: Regression

Ch. 11.1, 11.3.1-11.3.2 in textbook | Slides

**Recommended exercises**: 11.1, 11.2 (a), 11.3 (a), 11.5 (a) 11.8 (a,b), 11.10 (a,c), 11.11 (a,b), 11.12 (a,b,d) | Facit

**Seminar 11**: 11.2 (a), 11.3 (a), 11.5 (a), 11.8 (a,b), 11.12 (a,b,d)

**R-code**: Linear Regression

**Additional material**: R Manipulate | Example: Linear and quadratic regression

**Lecture 12**: Prediction

Ch. 11.2 in textbook | Slides

**Recommended exercises**: 11.2 (c), 11.3 (b,c), 11.4 (b,c,d), 11.5 (b,c), 11.8 (c) | Facit

**Seminar 12**: 11.2 (c), 11.3 (b,c), 11.4 (b,c,d), 11.8 (c)

**Additional material**: Seminar 12 Example

### Computer labs

In computer labs the participants are expected to work in groups. Sign up for the groups on LISAM (see Signup). The reports should be submitted on LISAM (see Submissions). See LISAM for submission deadlines.**Lab 1**: Simulation Lab

**Lab 2:**Estimation Lab

**Lab 3:**Bayesian inference Lab

### Other matherials

Page responsible: Maryna Prus

Last updated: 2022-10-14