Let X N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = −1) = P(Z = 1) = 1/2) be independent of X. Let Y=ZX. What is the distribution of Y? Show that X and Y are uncorrelated. Are X and Y independent?
Let X N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = −1) = P(Z = 1) = 1/2) be independent of X. Let Y=ZX. What is the distribution of Y? Show that X and Y are uncorrelated. Are X and Y independent?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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Transcribed Image Text:Let X~ N(0, 1), and let Z
1/2) be independent of X. Let Y
Y are uncorrelated. Are X and Y independent?
=
Unif{−1, 1} (i.e. P(Z = −1) = P(Z
1)
ZX. What is the distribution of Y? Show that X and
=
=
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