Course detail
Probability and Statistics
FIT-IPTAcad. year: 2019/2020
Classical probability. Axiomatic probability. Conditional probability. Total probability. Bayes' theorem. Random variable and random vector. Characteristics of random variables and vectors. Discrete and continuous probability distributions. Central limit theorem. Transformation of random variables. Independence. Multivariate normal distribution. Descriptive statistics. Random sample. Point and interval estimates. Maximum likelihood method. Statistical hypothesis testing. Goodness-of-fit test. Analysis of variance. Correlation and regression analyses. Bayesian statistics.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
- Written tests: 30 points.
- Final exam: 70 points.
Exam prerequisites:
Get at least 10 points during the semester.
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
- recommended prerequisite
Mathematical Analysis 1 - recommended prerequisite
Discrete Mathematics - recommended prerequisite
Mathematical Analysis 2
Basic literature
Recommended reading
Anděl, J.: Statistické metody. Praha: Matfyzpress, 1993. (CS)
Anděl, J.: Základy matematické statistiky. Praha: Matfyzpress, 2005. (CS)
Casella, G., Berger, R. L.: Statistical Inference. Pacific Grove, CA: Duxbury Press, 2001. (EN)
Fajmon, B., Hlavičková, I., Novák, M., Vítovec, J.: Numerická matematika a pravděpodobnost (Informační technologie), VUT v Brně, 2016 (CS)
Hlavičková, I., Hliněná, D.: Matematika 3. Sbírka úloh z pravděpodobnosti. VUT v Brně, 2015 (CS)
Hogg, R. V., McKean, J., Craig, A. T.: Introduction to Mathematical Statistics. Boston: Pearson Education, 2013. (EN)
Likeš, J., Machek, J.: Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1988. (CS)
Montgomery, D. C., Runger, G. C.: Applied Statistics and Probability for Engineers. New York: John Wiley & Sons, 2011. (EN)
Neubauer, J., Sedlačík, M., Kříž, O.: Základy statistiky. Praha: Grada Publishing, 2012. (CS)
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Introduction to probability theory. Combinatorics and classical probability.
- Axiomatic probability. Conditional probability and independence. Probability rules. Total probability, Bayes' theorem.
- Random variable (discrete and continuous), probability mass function, cumulative distribution function, probability density function. Characteristics of random variables (mean, variance, skewness, kurtosis).
- Discrete probability distributions: Bernoulli, binomial, hypergeometric, geometric, Poisson.
- Continuous probability distributions: uniform, exponencial, normal. Central limit theorem.
- Basic arithmetics with random variables and their influence on the parameters of probability distributions.
- Random vector (discrete and continuous). Joint and marginal probability mass function, cumulative distribution function, probability density function. Characteristics of random vectors (mean, variance, covariance, correlation coefficient). Independence. Multivariate normal distribution.
- Descriptive statistics. Data processing. Characteristics of central tendency, variability and shape. Moments. Graphical representation of the data.
- Random sample. Point estimates. Maximum likelihood method.
- Interval estimates. Statistical hypothesis testing. One-sample and two-sample tests (t-test, F-test).
- Goodness-of-fit test. Analysis of variance (ANOVA). One-way and two-way ANOVA.
- Correlation and regression analyses. Linear regression. Pearson's and Spearman's correlation coefficient.
- Bayesian statistics. Conjugate prior. Maximum a posteriori probability (MAP) estimate. Posterior predictive distribution.