Let X and Y be two independent N(0,1) random variables and consider Z = 3 +X+ 2XY² , W = 5 + X. Then Cov(Z, W) = Hint:Cov(X, X) = Var(X), Cov(X+c, Y) = Cov(X, Y) and Cov(X +Y,Z) = Cov(X,2) + Cov(Y,Z) O None of the other options Оз O 1
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- Let X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random variables. Find theLet X and Y be two independent N(0,1) random variables and consider Z = 3+ X + YX , W = 3 + Y. Then Cov(Z, W) = Hint:Cov(X, X) = Var(X), Cov(X+c, Y) = Cov(X, Y) and Cov(X + Y, Z) = Cov(X,2) + Cov(Y,Z) 1 None of the other options 3Let X ~ Binom(16, 1/4 ) and Y~Geom( 1/2 ) be two independent random variables. Compute(i) Cov(2X, 3Y ),(ii) Cov(X, 4X).
- Suppose X and Y are independent random variables with E(X) =2, E(Y)=3,V(X)=4,V(Y)=16. Finda)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y) d)COV(X,5X-Y)Is cov(X, Y) random?Q/ Let V=X+ Y and U=X - Y are random variables, then the condition which make the covariance C(U,V)=0 is a) Var(x)=Var(y) b) U and V are independent
- Let X1, X2, X3 be random variables such that Var(X1) = 5, Var(X2) = 4, Var(X3) = 7, cov(X1, X2) = 3, cov(X1, X3) = -2 and X2 and X3 are independent. Find the covariance between Y1 = X1 – 2X2 + 3X3 and Y2 = -2X1 + 3X2 + 4X3. %3DLet X and Y are two random variables. Find Var(2X – 3Y ) Select one: a. Var(2X - 3Y) = 4Var(X) – 12Cov(X, Y ) + 9Var(Y ) b. Var( 2X -3 Y) = 2Var(X) – 6Cov(X, Y ) + 3Var(Y ) c. var(2X -3Y ) = 2Var(X) – 3Var(Y ) d. Var(2X -3Y) = 2Var(X) + 6Cov(X, Y ) + 3Var(Y ) e. var(2x - 3y ) =4Var(X) + 12Cov(X, Y ) + 9Var(Y )Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.
- Let X and Y be two random variables and let r, s, t, and u be real numbers. a. Show that Cov(X+s, Y+u) = Cov(X,Y)b. Show that Cov(rX, tY) = rtCov(X,Y)c. Show that Cov(rX +s, tY + u) = rtCov(X,Y)Show that for two random variables X and Y, 2 2 var(aX+by) =a²o²+b²oy² + 2abCx X Y XY where a and b are real constants.X and Y are discrete random variables. If var(X)= var(Y) = o², cov(X,Y)=, find var(2X-3Y)