Download STATISTICS- 2014/15 Edoardo Otranto 1. Basic Probability concepts

STATISTICS- 2014/15
Edoardo Otranto
1. Basic Probability concepts: outcome, sample space, event, probability, conditional
probability, independent events, multiplication rule, addition rule
2. Random variables: discrete an continuous random variables, probability distribution,
probability density function, cumulative distribution function, expectation, variance
3. Bivariate random variables: joint probability function, marginal distributions,
independence, covariance, correlation
4. Random vectors: joint density, covariance matrix, linear transformations
5. Functions of Random variables: discrete to discrete, continuous to discrete, continuous to
continuous
6. Specific univariate distributions: discrete uniform, continuous uniform, normal, Chi
squared, Student t, Fisher F, Bernoulli, Binomial
7. Estimation theory: point estimation, finite properties, large sample distribution theory,
interval estimation
8. Hypothesis testing: null and alternative hypothesis, first and second type errors, size,
significance level, uniformly most powerful test, tests based on likelihood functions
9. Multivariate Normal distribution bivariate case, general case, linear functions of a Normal
vector, marginal distributions, conditional distributions
Reference books:
Mood-Graybill-Boes: Introduction to the Theory of Statistics, McGraw-Hill
Greene: Econometric Analysis (Statistical appendices), Prentice Hall