Course title in Estonian
Tõenäosusteooria ja matemaatiline statistika I
Course title in English
Theory of Probability and Mathematical Statistics I
approximate amount of contact lessons
lecturer of 2019/2020 Spring semester
õppejõud on määramata
lecturer of 2020/2021 Autumn semester
lecturer not assigned
Mathematics and statistics focus subject. Objective is to give an overview of the main methods stemming from the theory of probability.
Brief description of the course
Random events and their probability. Elementary rules of probability. Total probability formula, Bayes´ theorem. Discrete random variable. Binomial distribution. Distribution and density function of a random variable. Geometric probability and uniform distribution. Expection, variance and standard deviation of a random variable. Random vector, its distribution and density function. Sum and product of two random variables, their expection and variance. Covariance. Poisson distribution. Normal distribution. The central limit theorem. Normal approximation to the binomial. Chebyshev inequality. Law of large numbers. Statistical probability. Population, sample, empirical distribution function. Estimation of a population parameter.
Acquiring of the theory, solving problems and exercises
Learning outcomes in the course
After passing the course the student is able to define the main notions of probability and statistics, knows main formulas and is able to prove theorems taught at the coursse; is able to solve exercises about probability; is able to find point estimates and interval estimates, distribution functions, density functions of the distribution, Pearson and Spearman correlation coefficents.
Admission to the exam permitted once the two class tests and home tasks have been successfully completed. Written examination is worth 50% of the total number of points.
The course is a prerequisite
Gurski, J. 1986 Tõenäosusteooria ja matemaatilise statistika elemendid.
Jõgi, A. Tõenäosusteooria 1.osa. Tallinn: TTÜ;
Tammeraid, I. 2004 Tõenäosusteooria ja matemaatiline statistika. Tallinn: TTÜ;
Tiit, E. 1995 Tõenäosusteooria lühikursus. Tallinn, Avita;
Ross, S. M. 2002 A first course in probability. Prentice Hall.