# Mathematical Statistics

## Notes for the master's course Mathematical Statistics I. Topics include set operations, laws of probability, conditional probability and Bayes theorem, discrete distributions, continuous distributions, bivariate and multivariate distributions, distributions of functions of random variables, sampling distributions, moment generating functions, and laws of large numbers and central limit theorem. Mathematical Statistics

## Chapter 6. Sampling Distribution and Limit Theorems

We observe a random sample from a probability distribution of interest and want to estimate its properties. The CLT also comes into place. Mathematical Statistics

## Chapter 5. Functions of Random Variables

Finding the distribution of a real-valued function of multiple random variables. There's the method of distribution functions, transformations and moment generating functions. Mathematical Statistics

## Chapter 4. Multivariate Probability Distributions

Joint probability distributions of two or more random variables defined on the same sample space. Also covers independence, conditional expectation and total expectation. Mathematical Statistics

## Chapter 3. Continuous Random Variables and Their Probability Distributions

PDF, CDF, expectation, variance and MGF of the uniform, normal and exponential distributions. Also two approximations for the binomial distribution. Mathematical Statistics

## Chapter 2. Discrete Random Variables and their Probability Distributions

PMF, CDF, expectation, variance and MGF of Bernoulli, Binomial, Geometric and Poisson random variables. Mathematical Statistics

## Chapter 1. Probability

An introduction to the concept of the probability of an event. Set operations, axioms of probability, conditional probability and Bayes' rule.