Luke Stein Stanford graduate economics core (2006–7) Reference and review (last updated September 29, 2009)

Contents
1 Econometrics . . . . . . . . . . . . . . 1.1 Probability foundations . . . . . . . . Basic set theory Disjointness Partition Sigma algebra Probability function Probability space Counting Conditional probability Bayes’ Rule Independence of events Mutual independence of events Random variables . . . . . . . . . . . Random variable Random vector Measurability Smallest σ-field Independence of r.v.s Independence of random vectors Mean independence Cumulative distribution function Probability mass function Marginal pmf Conditional pmf Probability density function Marginal pdf Conditional pdf Borel Paradox Stochastic ordering Support set Transformations of random variables . Transformation R1 → R1 Transformation R2 → R2 Convolution formulae Probability integral transformation Properties of random variables . . . . Expected value, mean Conditional expectation Two-way rule for expectations Law of Iterated Expectations Median Mode Symmetric distribution Moment Variance Multivariate variance Conditional variance 4 4

Standard deviation Covariance Multivariate covariance Correlation Skewness Kurtosis Moment generating function Characteristic function Other generating functions 1.5 Distributions . . . . . . . . . . . . . . Normal distribution Bivariate normal distribution Multivariate normal distribution Chi squared distribution Student’s t distribution Snedecor’s F distribution Lognormal distribution Exponential families Location and Scale families Stable distribution Random samples . . . . . . . . . . . . Random sample, iid Statistic Unbiased estimator Sample mean Sample variance Sample covariance Sample correlation Order statistic Samples from the normal distribution Convergence of random variables . . . Convergence in probability Uniform convergence in probability Little o error notation Big O error notation Order symbols Asymptotic equivalence