ABSTRACT
This chapter offers a review on some mathematical and statistical topics that will be essential for understanding the algorithms presented in Parts III and IV of this book.
Probability theory deals with the analysis of experiments that have distinct outcomes such as “heads” or “tails” as outcomes of tossing a coin, or the 52 outcomes of drawing a card from a standard deck of playing cards. The set of all possible outcomes of such an experiment is called the sample space, which is usually symbolized with the Greek letter Omega (Ω). Denoting the elements (the individual outcomes, also known as the elementary events of the experiment) as ei, we have that
Ω = {e1, e2, . . . , en} For instance, if we denote “heads” as eh and “tails” as et, then the sample
space of the coin-toss experiment is Ω = {eh, et}. For the card draw, Ω ={e1, e2, . . . , e52}, where each of the 52 elements ei symbolizes the drawing of one of the 52 cards.
