DS212_Chap5_Discrete_distributions

DS212_Chap5_Discrete_distributions - 1 Chapter 5 Discrete...

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Unformatted text preview: 1 Chapter 5 Discrete Probability Distributions Sada Soorapanth Spring 2010 2 Types of Random Variable Random Variable -- a numerical description of the outcome of an experiment Discrete Random Variable -- the set of all possible values is at most a finite or a countably infinite number of possible values Experiment Random variable (x) Possible values for the random variables Promote a magazine Number of new subscribers to a magazine 0, 1, 2, 3, 4,… Inspect a shipment of 50 radios Number of defective radios 0, 1, 2, 3, 4,…, 49, 50 Determine the risk of heart disease Gender of the patient with heart disease 0 (male), 1 (female) 3 Type of Random Variable (cont) Continuous Random Variable -- takes on values at every point over a given interval Experiment Random variable (x) Possible values for the random variables Fill a soft drink bottle Volume per bottle (max volume = 1.2 L) 0 ≤ X ≤ 1.2 L Operate a bank Elapsed time between arrivals of bank customers X ≥ Observe the impact of new economic policy Percent of the labor force that is unemployed 0 ≤ X ≤ 100 4 Example: Type of Variables Determine the type of the following random variables; a) Throw two dice over and over until you roll a double six; X = the number of throws. b) Take a true-false test with 100 questions; X = the number of questions you answered correctly. c) Invest $10,000 in stocks; X = the value, to the nearest $1, of your investment after a year. d) Select a group of 50 people at random; X = the average height (in m) of the group 5 Probability Distribution Probability Function, P(X=x) Provides the probability that the random variable assumes a particular value. Equivalent to the relative frequency of the histogram Probability Distribution, P(X) for all x’s Lists all the outcomes of an experiment and their associated probabilities. Cumulative Probability Function, P(X≤ x) Provides the probability that the value of random variable is less than or equal to a particular value. 6 Type of Probability Distribution Discrete Distribution constructed from discrete random variables Continuous Distribution constructed from continuous random variables To be discussed in the next chapter 7 Discrete Distribution -- Example 1 2 3 4 5 0.37 0.31 0.18 0.09 0.04 0.01 Number of Crises (X) Probability P(X) Distribution of Daily Crises 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 P r o b a b i l i t y Number of Crises What is the probability that the number of crises per day will be less than or equal to 3 i.e. P(X ≤ 3) ? 8 Requirements for a Discrete Probability Function 1. Probabilities are between 0 and 1, inclusively 2. Total of all probabilities equals 1 1 ≤ ≤ P X ( ) for all X P X ( ) over all x ∑ = 1 9 Requirements for a Discrete Probability Function -- Examples X P(X)-1 1 2 3 .1 .2 .4 .2 .1 1.0 X P(X)-1 1 2 3-.1 .3 .4 .3 .1 1.0 X P(X)-1 1 2 3 .1 .3 .4 .3 .1 1.2 PROBABILITY DISTRIBUTION : : A A B B C C 10...
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This note was uploaded on 09/10/2011 for the course DS 212 taught by Professor Saltzman during the Spring '08 term at S.F. State.

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DS212_Chap5_Discrete_distributions - 1 Chapter 5 Discrete...

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