# 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)

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)

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

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)

### 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