Let X be a normal random variable with parameters = 0 and 2 = 1,
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Let X be a normal random variable with parameters μ = 0 and σ2 = 1, and let I, independent of X, be such that P{I = 1} = 1/2 = P{I = 0}. Now define Y by
In words, Y is equally likely to equal either X or −X.
(a) Are X and Y independent?
(b) Are I and Y independent?
(c) Show that Y is normal with mean 0 and variance 1.
(d) Show that Cov(X, Y) = 0.
Transcribed Image Text:
X =1-X if I =1 if I = 0
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a No b Yes since f Y xI ...View the full answer
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