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: ProbabilityCh. 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 StatisticsCh. 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