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...

$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. $

Extracted 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.

Jun 11, 2022

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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...

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