Advanced econometrics

Chapter 3 : Probability theory

By Lund University

All the probability theory that we need for this course

Basic probability theory, review

This section has some elementary lectures on probability theory. Most of this should be known to you. We go straight to the definition of a random variable. Behind the scenes are concepts such as experiment, sample space, outcome, and probabilities. If you are interested, you can read more here: Probability.

Random variable

Distribution functions

Standard normal

Expected value of a discrete random variable

Expected value of a continuous random variable

The variance of a random variable

The expected value and variance of a linear function of a random variable

The normal distribution

Covariance, correlation and independence (intro)

Conditional expectation and conditional variance, introduction

Sample as a sequence of random variables

Random vectors

To do: Random vector, EV of RV, Variance of RV, EV and Variance of linear functions, vectors of conditional expectations.

Random vector

The variance of a random vector

Expected value and variance for random vectors

Expected value and variance for random vectors

The variance matrix must be positive semidefinite