a. Show that if X has a normal distribution with parameters and , then (a linear function

Question:

a. Show that if X has a normal distribution with parameters and , then (a linear function of X)

also has a normal distribution. What are the parameters of the distribution of Y [i.e., E(Y) and V(Y)]? [Hint:

Write the cdf of Y, , as an integral involving the pdf of X, and then differentiate with respect to y to get the pdf of Y.]

b. If, when measured in , temperature is normally distributed with mean 115 and standard deviation 2, what can be said about the distribution of temperature measured in ?

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Probability And Statistics For Engineering And The Sciences

ISBN: 9781133169345

8th Edition

Authors: Jay L Devore, Roger Ellsbury

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Question Posted: Sep 21, 2024 10:04 AM

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a. Show that if X has a normal distribution with parameters and , then (a linear function

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Probability And Statistics For Engineering And The Sciences

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