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Financial Modeling with Crystal Ball and Excel Chapter 4

CHAPTER 4 Selecting Crystal Ball Assumptions This chapter reviews basic concepts of probability and statistics using graphics from Crystal Ball’s distribution gallery, a portion of which is shown in Figure 4.1. If you have not had a class in basic probability and statistics at some point in your life or you need a refresher on these topics | 4 Selecting Crystal Ball Assumptions This chapter reviews basic concepts of probability and statistics using graphics from Crystal Ball s distribution gallery a portion of which is shown in Figure 4.1. If you have not had a class in basic probability and statistics at some point in your life or you need a refresher on these topics consult a business statistics textbook such as Mann 2007 . This chapter is intended to show the basics of how to specify probability distributions to be used as stochastic assumptions with Crystal Ball. Version 7.2 of Crystal Ball has 20 distributions from which to choose when defining assumptions. To see them click the All button at the upper left of the distribution gallery. Six basic distributions are described here along with the binomial distribution. CRYSTAL BALL S BASIC DISTRIBUTIONS Yes-No Probabilists named the Bernoulli distribution in honor of the mathematician who showed analytically around 1700 the truth of the intuitive notion that when a fair coin is tossed repeatedly it will come up heads about 50 percent of the time. It is perhaps the simplest of all probability distributions. The random variable Y has the Bernoulli distribution if it can take only one of two possible values y 0 or y 1. The value y 1 is called a success and y 0 is called a failure in probability parlance. In Crystal Ball the Bernoulli distribution is known as the yes-no distribution. Crystal Ball calls y 1 yes and y 0 no because these terms often make sense in a modeling context. For example Figure 4.2 shows Crystal Ball s yes-no distribution for Pr yes 0.5 where y represents the number of heads obtained in one toss of a fair coin. Yes means a head was tossed so y 1 while no means a tail was tossed so y 0. Now consider the type of situation that drew Bernoulli s interest. The spreadsheet segment in Figure 4.3 shows a simple model to be used for finding the number of heads observed when tossing a fair coin five times. Each of the assumptions in cells B3 B7