M670_4(Discrete Distributions)

M670_4(Discrete Distributions) - 1 Discrete Probability...

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Unformatted text preview: 1 Discrete Probability Distributions k MGMT 670: Business Analytics Krannert School of Management Purdue University 2 Random Variables Numerical description of the outcome of an experiment Classified as either discrete or continuous Discrete random variable : either a finite number of values or an infinite sequence of values such as 0, 1, 2, 3, . Continuous random variable : any numerical value in an interval or collection of intervals. 3 Examples of Discrete Random Variables Experiment : Make 100 sales calls, and record the number of sales made. Possible values: 0, 1, 2, 3, , 100 Experiment : Operate a restaurant for one day, and record the number of customers entered. Possible values: 0, 1, 2, 3, Experiment : Sell an automobile, and record the gender of the customer. Possible values: male, female 4 Examples of Continuous Random Variables Experiment : Operate a bank, and record the time between customer arrivals ( X ). Possible values: X 0. Experiment : Observe a machines working hours, and record the utilization rate in an eight-hour workday ( Y ). Possible values: 0 Y 100% 5 Discrete Probability Distributions List of all possible pairs of ( xi, f(xi )) where xi = a value of the random variable X f ( xi ) = probability of getting value of xi f ( xi ) is referred to as the probability mass function . Conditions for the probability mass function: Described with a table, graph, or equation . 1 ) ( 1 ) ( = i i i x f x f 6 Example: Oil Commodities A commodities investor is concerned with the price of oil for the coming year. The investor believes there are four possible scenarios for the oil market in the coming year: high demand, moderate demand, no growth, or moderate contraction. She estimates that the price of oil per barrel in each case will be $78, 73, 63, and 50, respectively. Also, she has assessed that the probabilities of these outcomes are 0.10, 0.50, 0.25, and 0.15, respectively. 7 Distribution of Oil Price (X) Economic Outcome Price, xi Probability High Demand 78 0.10 Moderate Demand 73 0.50 No Growth 63 0.25 Moderate Contraction 50 0.15 Total 1.00 8 Expected Value of Discrete Random Variable Weighted average of all possible values = = i i i x f x X E ) ( ) ( x i p ( x i ) x i p ( x i ) 78 0.10 7.80 73 0.50 36.50 63 0.25 15.75 50 0.15 7.50 Sum 1.00 67.55 = E ( X ) 9 Variance of Discrete Random Variable Weighted average of squared deviations from the mean ( 29 ( 29 2 2 2 Var ( ) ( ) i i i (X) E X E X x E X f(x ) = =- =- x i p ( x i ) x i...
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This note was uploaded on 10/17/2011 for the course MGMT 670 taught by Professor Tawarmalani during the Spring '11 term at Purdue.

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M670_4(Discrete Distributions) - 1 Discrete Probability...

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