Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X,Y ) = 1. (a) Find Cov(2X −Y,X + 3Y ). (b) Find ρ(2X −Y,X + 3Y ) (the correlation between 2X −Y and X + 3Y ).
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Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X,Y ) = 1.
(a) Find Cov(2X −Y,X + 3Y ).
(b) Find ρ(2X −Y,X + 3Y ) (the
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.The joint pmf of X and Y is f(x, y) = 1/6, 0 ≤ x+y ≤ 2, where x and y are nonnegative integers. Compute Cov(X, Y) and determine the correlation coefficient.Make sure to show the correct work and solution: Suppose P(X = 0, Y = 0) = 1/3, P(X = 0, Y = 3) = 1/3, and P(X = 6, Y = 3) = 1/3. Find Cov(X, Y ) and the correlation ρ of X and Y .