Probability and statistics (MASTER)

The concepts of probability and statistics are the basis for financial modeling. The course presents the essential concepts of probability necessary for risk management. The statistical part of the course deals with statistical models, parameter estimation, data analysis and their relevance for financial modeling. Concept of accuracy of estimation, diagnistics, hypothesis testing and back testing models are part of the course.

Probability
1. Events, probability, conditional probability, independence.
2. Random variables and their distributions.
3. Discrete joint distributions, continuous joint distributions, independence, functions of random vectors, conditional distributions. 4. Expectation, variance, covariance, conditional expectation, conditional variance.
5. Approximation of distributions, central limit theorem.

Statistics
1. Sampling, standard error, confidence intervals.
2. Statistical models, parameters, estimation.
3. Estimation techniques,maximum likelihood method, properties of estimators, asymptotic properties of estimators.
4. Hypothesis testing, examples of tests, properties of tests, Wilks' likelihood ratio test.
5. Linear regression and its generalizations, Gauss-Markov theorem.