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True or false? and explain please. (i) Let Z = 2X + 3. Then, Cov(Z,Y )...

True or false? and explain please.

(i) Let Z = 2X + 3. Then, Cov(Z,Y ) = 2Cov(X,Y ).
(j) If X,Y are uncorrelated, and Z = −5−Y + X , then V ar(Z) = V ar(X) + V ar(Y ).
(k) Let X,Y be uncorrelated random variables (Cov(X,Y ) = 0) with variance 1 each. Let A = 3X + Y . Then, V ar(A) = 4.
(l) If X and Y are uncorrelated (meaning that Cov[X,Y ] = 0) but are not jointly Gaussian, then E[X|Y ] = E[X] always.

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Answer #1

(i). True

(j). True

(k). False

(l). False

  

  

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