Chapter 6 notes

Chapter 6 notes - Chapter 6 Discrete Probability Distributions Characteristics of a Probability Distribution 1 The probability of a particular

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Chapter 6: Discrete Probability Distributions Characteristics of a Probability Distribution: 1. The probability of a particular outcome is between 0 and 1. 2. The outcomes are mutually exclusive events. 3. The list is exhaustive. So the sum of the probabilities of the various events is equal to 1. The Mean of a Probability Distribution: µ = ∑ [xP(x)] The Variance of a Probability Distribution: σ 2 = ∑ [(x - µ) 2  P(x)] The computational steps are: 1. Subtract the mean from each value and square this difference. 2. Multiply each squared difference by its probability. 3. Sum the resulting products to arrive at the variance. 4. To get the standard deviation, take the square root of the variance ( σ 2 ) X(sales next month) P(x) xi * P(xi) xi     2    * P(xi)     12.5 0.10 1.25 15.625 15.5 0.20 3.1 48.05 25.0 0.25 6.25 156.25 32.7 0.30 9.81 320.787 40.0 0.15 6 240 1 26.41 780.712 Short-cut: Var(x): ∑ xi 2  * P(xi) – [E(x)] 2 = 780.712 – [26.41] 2 = 780.712 – 697.4881 Var(x) = 88.2239 St dev (x) = square root of 88.2239 =  9.1227 Binomial Probability Distribution 1. An experiment is repeated  “n” times (n = # of trials)
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2. Every time the experiment is repeated, only 2 outcomes are possible (S= success,  F= failure) 3. The probability of success is always the same in every trial of the experiment. a.
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This note was uploaded on 04/19/2008 for the course ECON 219 taught by Professor Valencia during the Spring '08 term at Slippery Rock.

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Chapter 6 notes - Chapter 6 Discrete Probability Distributions Characteristics of a Probability Distribution 1 The probability of a particular

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