Chapter 7 Continuous Distributions

Chapter 7 Continuous Distributions - Click to edit Master...

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Unformatted text preview: Click to edit Master subtitle style Professor Thomas R. Professor Thomas R. 11 Continuous Distributions Professor Thomas R. Sexton College of Business Stony Brook University Professor Thomas R. Professor Thomas R. 22 Continuous Distributions For some random variables, the support is a continuous set of numbers, such as: l The set of all real numbers l The set of all nonnegative real numbers l The set of all real numbers between a and b For such random variables, the tools we use for discrete random variables do not Professor Thomas R. Examples Assets Revenue Profit Cost Household income SAT scores Length Professor Thomas R. 33 Professor Thomas R. Professor Thomas R. 44 Cumulative Distribution Function (CDF) For continuous random variables, we define the cumulative distribution function , F ( x ), to be the probability that the random variable X is less than or Professor Thomas R. Example: Corporate Profit Let X = last years profit of a randomly selected firm in the electronics industry. F ( x ) = P (firms profit x ) for any x + F ($20 million) = P (firms profit $20 million) F ($10 million) = P (firms profit $10 Professor Thomas R. 55 Professor Thomas R. Professor Thomas R. 66 Graph of F ( x ) x F ( x ) 1 Professor Thomas R. Probability Density Function (PDF) The PDF tells us how densely the probability is packed near each point, x. If the random variable, X, is likely to occur near a point x, then the PDF will be high near x. The PDF will be low in areas where X is unlikely to fall. Professor Thomas R. 77 Professor Thomas R. Professor Thomas R. 88 Probability = Area Under Density f ( u ) u b ) ( P b X a a Professor Thomas R. Professor Thomas R. 99 Probability = Area Under Density u f ( u ) x ( 29 x F x X = ) ( P Professor Thomas R. Professor Thomas R. 1010 Example: Uniform Distribution Suppose that the flying time from Los Angeles International Airport (LAX) to McCarran International Airport (LAS) in Las Vegas is uniformly distributed between 60 and 70 minutes. What is the probability that the flying time will be between 62 and 65 minutes? Professor Thomas R. Professor Thomas R. 1111 Graph of f ( x ) x 60 f ( x ) 0.1 70 60 ; 10 1 ) ( = x x f 70 Professor Thomas R. Professor Thomas R. 1212 Graph of F ( x ) x 60 F ( x ) 1 70 60 ; 10 60 ) ( - = x x x F 70 Professor Thomas R. Professor Thomas R. 1313 P(62 x X 65) x 60 f ( x...
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This note was uploaded on 09/17/2009 for the course BUS 215 taught by Professor Thomassexton during the Fall '09 term at SUNY Stony Brook.

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Chapter 7 Continuous Distributions - Click to edit Master...

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