Let X and Y be two random variables such that E(X) = 1, E(Y) = 2, Var(X) = 34, and Var(Y) = 2. If Cov(X,Y) = -4, then E(X+Y) = 9/2.
Added by Antonio C.
Step 1
First, we can use the formula for the covariance between two random variables: cov(1,%,) = E[(1 - E(1))(%-E(%))] = E(1%) - E(1)E(%) = -4 We know E(1) = 1 and E(%) = 2Y+1, so we can substitute: E(1(2Y+1)) - 1(2Y+1) = -4 2E(Y) + E(Y) - 1 = -4 3E(Y) = -3 E(Y) = Show more…
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