ABSTRACT
This chapter deals with a number of topics that on one hand seem abstract and theoretical but on the other hand are essential for the practical application of probability to real life problems. We begin with the topic of inequalities. The inequalities developed here are well known and are used to estimate or bound the probability for random variables when only partial information (e.g., mean and variance) is known for the distribution. As such they provide tools for calculating or bounding probability from limited real data and also for proving general results that make as few assumptions as possible about the properties of the random variables.
