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Problem 5) Show that if X is a Normal random variable with a meanµ and standard deviation o, then the random variable Y defined by: Y = aX + b, where a and b are real numbers with a # 0, is also Normally distributed. What are the mean and the standard deviation of Y?

Problem 5) Show that if X is a Normal random variable with a meanµ and standard deviation o, then the random variable Y defined by: Y = aX + b, where a and b are real numbers with a # 0, is also Normally distributed. What are the mean and the standard deviation of Y?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 5) Show that if X is a Normal random variable with a meanu and standard deviation o, then the random variable Y defined by: Y = aX + b, where a and b are real numbers with a + 0, is also Normally distributed. What are the mean and the standard deviation of Y? (Hint: write the cdf of Y; that is, P(Y < y) , as an integral involving the pdf of X. Then differentiate with respect to y to get the pdf of Y.)
Transcribed Image Text:Problem 5) Show that if X is a Normal random variable with a meanu and standard deviation o, then the random variable Y defined by: Y = aX + b, where a and b are real numbers with a + 0, is also Normally distributed. What are the mean and the standard deviation of Y? (Hint: write the cdf of Y; that is, P(Y < y) , as an integral involving the pdf of X. Then differentiate with respect to y to get the pdf of Y.)
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