siness, eco- nomics, and finance! The underlying motivation of maximum-entropy models (MEM) is to derive, heuristically, the PDF of a complex random process by using available data samples observed from reality. These experimental data are then used as constraints to compute the maximum-entropy PDF, elegantly referred to as epistemic. The philosophy and rationale of the maximum-entropy principle approach is: "Given facts or relations concerning events, which are verified in the physical world, what is the best statistical model available to predict the rest?" The issue of maximizing entropy is revisited in Chapter 5 when considering continuous sources. Exercises 4.1 (B): What is the entropy in the action of picking, at random, one card out of a 32-card deck? What is the entropy for picking a hand of four cards? 4.2 (B): A bag contains eight balls, including one red, two blue, two green, and three yellow ones. The events consist in picking, at random, a ball from the bag, seeing the color, and then replacing the ball. What is the entropy of the source? 4.3 (M): Download from any website the text of the US Declaration of Independence, www.ushistory.org/declaration/document/index.htm, www.law.indiana.edu/uslawdocs/declaration.html, www.loc.gov/rr/program/bib/ourdocs/DeclarInd.html, www.archives.gov/exhibits/charters/declaration.html, 18 See, for instance:www.answers.com/topic/principle-of-maximum-entropy?cat=technology&hl?functions hl?derivation=&hl?partition=, www.answers.com/maximum+entropy+probability+distribution?cat: technology. Entropy from, "When in the Course of human events " to " our Fortunes and our sacred Honor." What is the entropy of the selected text, as viewed as a source of 26 + 1 characters (including space)? What is the entropy of the selected text, without the space character? (Computing method clue: see Chapter 4, note 11.) 4.4 (M): Copy into a text file a "very big" prime number, for instance, a large "Mersenne," which you can download from the websites: www.mersenne.org/, www.isthe.com/chongo/