ABSTRACT
This chapter is the heart of the text. It starts with the definition of random variables – both discrete and continuous. Cumulative distributions are defined and the associated probability mass functions and probability density functions are explained. Survivor functions are defined. Then, the formulation of empirical distributions is demonstrated for the discrete case, and this is followed by a comprehensive presentation of seven specific families of discrete distributions – the ones that are most commonly applied. Next, the corresponding constructions for continuous random variables are presented, including seven of the most commonly applied models and specifically emphasizing the importance of the normal distribution and its computation. Brief discussions of conditional probability, independence, residual life distributions and hazard functions complete the chapter.
