Probability Theory

Basic information

Workload: 

90 hours

Prerequisite: 

Calculus in several variables.

Syllabus: 

Sample events and spaces. Independence, conditional probabilities and product spaces. Random variable. Discrete random variables (Bernoulli, binomial, Poisson, geometric and hypergeometric) and continuous (uniform, exponential, gamma, normal). Hope and variance. Covariance and correlation. Poisson process. Conditional probability, conditional expectation. Sequences of random variables: notion, concepts of convergence. Laws of Great Numbers: concept, the weak law, the strong law; applications. Central Limit Theory - situation of the problem; Central Limit Theorem; applications. Sample distributions (t, chi-square and F). Introduction to Statistical Inference.

 

Teaching Plan

Bibliography

Mandatory: 

•    Ralph Teixeira and Augusto César Morgado. Class notes. 
•    W. Bussab and P. Morettin. Basic Statistics: Probability and Inference. Pearson, 2010 
•    Paul Meyer. Probability: applications to Statistics. Technical and Scientific Books, 1983. 

Complementary: 

•    Sheldon Ross. Probability: a modern course, with applications. Artmed, 2010. 
•    C. Morgado et al. Combinatory Analysis and Probability. SBM, 2001. 
•    Barry R. James. Probability: an intermediate course. IMPA, 1996. 
•    Kai Lai Chung and Farid AitSahlia. Elementary probability theory: with stochastic processes and an introduction to mathematical finance. Springer, 2003. 
•    R.V. Hogg and E.A.Tannis. Probability and statistical inference. Prentice Hall, 2010.