Hudson Derek J. Lectures on elementary statistics and probability

Geneva: CERN, 1963. — 103 p.This set of six lectures is a summary of some of principal results in the theory of random variables. The arguments used are based on the axioms of the theory of probability, which re presented in the classical way. Discrete and continuous distributions are defined, and at the end the chi2 and t distributions are evaluated. Moment generating functions are used as a tool to derive new distributions and to give an abbreviated proof of the central limit theorem.
In the course of the lectures, some statistical concepts are introduced which form the basis of the more advanced science of statistical interference. The intention is to examine these concepts further in a second set of lectures, to be given later.Introduction to probability
Discrete distributions
Continuous distributions
The expected value of a random variable
The moments of a random value
The joint probability distribution of two or more random variables
The law of large numbers
Distribution of a function of a random variable
The goodness of fit test