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Unformatted text preview: Chapter 5: Discrete probability distributions • Probability Distributions • Mean, Variance, Standard Deviation, and Expectation • The Binomial Distribution • Other Types of Distributions Probability Distributions • A random variable is a variable whose values are determined by chance. • A discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. The probabilities are determined theoretically or by observation. Example: If one tossed three coins, where X is the number of heads appear, find and plot the probability distribution of X. Solution: S={HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} each outcome with probability 1/8, and X takes the values 0, 1, 2 and 3. The probability distribution of X is Two Requirements for a Probability Distribution 1. The sum of the probabilities of all the events in the sample space must equal 1; that is , ∑ g1842 g1876 g3404 1 . 2. The probability of each event in the sample space must be between or equal to 0 and 1. That is, 0 ≤ P ( X ) ≤ 1. Example: Determine whether each distribution is a probability distribution. Solution: a) Yes, Why? B)No, Why? C) Yes, Why? D) No, Why? Mean, Variance, Standard Deviation, and Expectation Formula for the Mean of a Discrete Probability Distribution: Example: The probability distribution shown represents the number of trips of five nights or more that American adults take per year. Find the mean of the number of trips....
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 Spring '12
 johnanderson
 Statistics, Binomial, Poisson Distribution, Probability, Standard Deviation, Variance, Probability distribution, Probability theory, Discrete probability distribution

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