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12776 Probability Calculus - Three-year degree in Statistical Sciences and Techniques

Center

Faculty of Mathematics

Departament

Statistics and Operational Research

Lecturers in charge

Sin datos cargados

Met. Docent

Met. Avaluació

Continuos evaluation - -

Bibliografia

DeGroot, M.H.; Probabilidad y Estadística, 2ª Ed. Addison Wesley
Iberoamerica, 1988.

Kelly, D.G., Introduction to Probability. Macmillan Publishing Company,
1994.

Pitman, J.; Probability, Springer Verlag. New York, 1993.

Rice, J.A., Mathematical Statistics and Data Analysis, 2ª Ed., Belmont:
Duxbury Press, 1995

Ross, S.M.; A first course in Probability, 3ª Ed. Macmillan Publishing
Company, 1988.

Stirzaker, D., Elementary probability, Cambridge University Press, 1994.

Continguts

Objectives
Introduce the concepts, terminology and basic properties of the Calculus of
Probabilities as a mathematical model which deals with the study of
Natural phenomena that depend on randomness. Familiarise the student with
the laws that control random phenomena and give them the basic tools
which will allow them to calculate probabilities associated with events of interest.
Detailed study will be made of variable models and randomness vectors.

Theory Program
1.- Probability
Causality and randomness. Experiment and sample space. Events.
Probability. Properties of probability. Conditioned probability.
Independence of events.

2.- Randomness Variables
Randomness variables. Induced probability. Function of probability distribution.
Discreet randomness variable: function and quantity. Continuous randomness variable: density function of probability. Functions of a randomness variable.

3.- Randomness Vectors
Randomness vectors. Induced probability. Functions of joint and marginal distribution.
Discreet random vector: function of joint quantity. Continuous randomness vector: function of joint density. Functions of randomness variables. Independence. Conditioned distributions. Statistical extremes of order.

4.- Expectancy
Expectancy of a randomness variable. Moments of a randomness variable.
Disequalities. Expectancy of a randomness vector. Moments. Conditioned expectancy and