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Let X and Y be independent, identically distributed RVs with the stan- dard normal PDF S(x) = xER. Find the joint PDF of U = X + Y and V = X – Y. Show that U and V are independent and write down the marginal distribution for U and V. Let if X > 0. Z= -\Yl. if X < 0. By finding F(Zs:) for :< 0 and :> 0, show that Z has a standard normal distribution. Explain briefly why the joint distribution of X and Z is not bivariate normal.

Let X and Y be independent, identically distributed RVs with the stan- dard normal PDF S(x) = xER. Find the joint PDF of U = X + Y and V = X – Y. Show that U and V are independent and write down the marginal distribution for U and V. Let if X > 0. Z= -\Yl. if X < 0. By finding F(Zs:) for :< 0 and :> 0, show that Z has a standard normal distribution. Explain briefly why the joint distribution of X and Z is not bivariate normal.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X and Y be independent, identically distributed RVs with the stan- dard normal PDF S(x) = Find the joint PDF of U = X + Y and V = X – Y. Show that U and V are independent and write down the marginal distribution for U and V. Let Jırı. if X > 0, Z= (-\Yl. if X <0. By finding P(Zs:) for :< 0 and :>0, show that Z has a standard normal distribution. Explain briefly why the joint distribution of X and Z is not bivariate normal.
Transcribed Image Text:Let X and Y be independent, identically distributed RVs with the stan- dard normal PDF S(x) = Find the joint PDF of U = X + Y and V = X – Y. Show that U and V are independent and write down the marginal distribution for U and V. Let Jırı. if X > 0, Z= (-\Yl. if X <0. By finding P(Zs:) for :< 0 and :>0, show that Z has a standard normal distribution. Explain briefly why the joint distribution of X and Z is not bivariate normal.
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