Description:
Sample spaces, probability and conditional probability, independence, random variables, expectation, distribution theory, sampling distributions, laws of large numbers and asymptotic theory, order statistics.
Required Book:
Statistical Inference (Second edition) by G. Casella and R.L. Berger. Duxbury, 2002.
Material: This material is mostly from Chapters 1-5 of the textbook
1. Probability Theory:
Set Theory. Probability Theory. Conditional Probability and Independence. Random Variables. Distribution Functions. Density and Mass Functions.
2. Transformations and Expectations:
Distribution of Functions of a Random Variable. Expected Values. Moments and Moment Generating Functions. Differentiating Under an Integral Sign.
3. Common Families of Distributions:
Introductions. Discrete Distributions. Continuous Distributions. Exponential Families. Locations and Scale Families. Inequalities and Identities.
4. Multiple Random Variables: Joint and Marginal Distributions. Conditional Distributions and Independence. Bivariate Transformations. Hierarchical Models and Mixture
Distributions. Covariance and Correlation. Multivariate Distributions. Inequalities.
5. Properties of a Random Sample:
Basic Concepts of Random Samples. Sums of Random Variables from a Random Sample. Sampling for the Normal Distribution. Order Statistics. Convergence Concepts. Generating a Random Sample.