Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
 AD2M01PMS Probability and Statistics Extent of teaching: 28+6 Guarantors: Roles: P,V Language ofteaching: CS Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 8 Semester: Z

Anotation:

The course covers probability and basic statistics. First classical probability is introduced, then theory of random variables is developed including examples of the most important types of discrete and continuous distributions. Next chapters contain moment generating functions and moments of random variables, expectation and variance, conditional distributions and correlation and independence of random variables. Statistical methods for point estimates and confidence intervals are investigated.

Study targets:

The aim of the course is to introduce students to basics of probability and statistics.

Course outlines:

 1 Events and probability. 2 Sample spaces. 3 Independent events, conditional probability, Bayes' formula. 4 Random variable, distribution functin, quantile function, moments. 5 Independence of random variables, sum of independent random variables. 6 Transformation of random variables. 7 Random vector, covariance and correlation. 8 Chebyshev's inequality and Law of large numbers. 9 Central limit theorem. 10 Random sampling and basic statistics. 11 Point estimation, method of maximum likehood and method of moments, confidence intervals. 12 Test of hypotheses. 13 Testing of goodness of fit.

Exercises outline:

 1 Events and probability. 2 Sample spaces. 3 Independent events, conditional probability, Bayes' formula. 4 Random variable, distribution functin, quantile function, moments. 5 Independence of random variables, sum of independent random variables. 6 Transformation of random variables. 7 Random vector, covariance and correlation. 8 Chebyshev's inequality and Law of large numbers. 9 Central limit theorem. 10 Random sampling and basic statistics. 11 Point estimation, method of maximum likehood and method of moments, confidence intervals. 12 Test of hypotheses. 13 Testing of goodness of fit.

Literature:

 [1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990. [2] Stewart W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press 2009.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Webpage: