Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions

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A2M01PMS	Probability and Statistics			Extent of teaching:	4+2
Guarantors:		Roles:	P,V	Language of teaching:	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:

https://moodle.fel.cvut.cz/courses/A2M01PMS

Subject is included into these academic programs:

Program	Branch	Role	Recommended semester
MPIB	Common courses	V	–
MPEEM1	Technological Systems	V	1
MPEEM5	Economy and Management of Electrical Engineering	V	1
MPEEM4	Economy and Management of Power Engineering	V	1
MPEEM3	Electrical Power Engineering	V	1
MPEEM2	Electrical Machines, Apparatus and Drives	V	1
MPKME1	Wireless Communication	P	1
MPKME5	Systems of Communication	P	1
MPKME4	Networks of Electronic Communication	P	1
MPKME3	Electronics	P	1
MPKME2	Multimedia Technology	P	1
MPKYR4	Aerospace Systems	V	1
MPKYR1	Robotics	V	1
MPKYR3	Systems and Control	V	1
MPKYR2	Sensors and Instrumentation	V	1

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Page updated 16.12.2019 07:51:55, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)