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Unformatted text preview: Chapter 5: Discrete Probability Distributions Page 1 of 4 What is a probability distribution? Probability Distribution gives all the possible outcomes and the probabilities associated with each. There are two (2) types of probability distributions. We have discrete and continuous distributions. The words discrete and continuous have the same meanings as they did in chapter 1. So a discrete probability distribution is a distribution for discrete variables/outcomes, i.e., the outcomes/variables that we can count and that end. A continuous distribution would be the one with continuous variables/outcomes, i.e. variables with infinite outcomes. No matter which distribution we are discussing, probabilities are not negative and are not bigger than one (1), and the total of the probabilities is one (1). Distributions can have known/given names or they may not. Regardless, once we know the distribution we can determine probabilities, means, and variances. For discrete distributions we use summations and for continuous distributions we use integrals to calculate these statistics. (An integral is analogous to summations in calculus.) In this chapter, we will focus our attention on discrete distributions. Discrete Probability Facts The discrete probability must meet the following criteria: (1.) 1 ) ( = x P The sum of the probabilities of our random variable x is 1. (2.) 1 ) ( x P The probabilities of our random variable x are between 0 & 1, inclusively. The following is an example of a discrete probability. The number of movies rented per person at MoviesRUs in a day. Variable x Probability P(x) 0 40 1 1 10 3 2 20 7 3 5 1 4 10 1 5 40 1 x is the variable we are keeping track of. P(x) is the probability for that outcome. For example, P(2) = 20 7 says the probability that our variable has the value 2 is 20 7 . It is valid because the sum of the probabilities is 1 and the probabilities are between 0 & 1. Although we are not given a list of values obtained like in chapter 3, we can still obtain the mean, variance and standard deviations. Mean, Variance & Standard Deviation Mean / Expected Value: = x x P ) ( We multiply each outcome times its probability. Then we add up all those products. Variance: ( ) = 2 2 ) ( x x P Subtract the mean from each outcome and square that result....
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- Spring '09