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lecturenotesweek9 - ISyE 2027 Probability with Applications...

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ISyE 2027 Probability with Applications Polly B. He Fall10, Week 9 Reading: Section 8.1-8.4 Transforming Discrete Random Variables Given a function of a random variable, we want to obtain the new distribution function and the probability mass function (or density function for the continuous case). Example 8.1.1 Consider an airplane with 150 seats. The number of customers has a discrete uniform distribution, say P ( X = j ) = 1 / 200 , j = 1 , 2 , . . . , 200. Let Y be the number of customers being turned away. Calculate the distribution function and the probability mass function for Y . Transforming Continuous Random Variables A simple example: Let X be the temperature expressed in degrees Celsius, then Y = 9 5 X +32 is the temperature in degrees Fahrenheit. If we know the distribution function of X (call it F X ) and the corresponding density function f X , what are the distribution and density functions of Y ? 1
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Rules for change-of-units transformation. Let X be a continuous random variable with distribution function F X
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