Suppose that X andY are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y?) = 30 and cov(2X – Y,4X – 3Y) = -12, then cov(-5X – 3, 2Y + 4) is equal to: Hint: cov(aX + br, сх + dr) %3 асV(х) + bdv (Y) + (be + ad)cov(X,Y) -64 -30 -120 -59
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- Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variablesSuppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???
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- Let X1,...,Xn be iid random variables with expected value 0, variance 1, and covariance Cov [Xi,Xj] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X1 +...+Xn.Suppose Xis a random variable with E(X) = 2, and E(X2) = 5. Compute the following quantities: a) Var(X) b) E(X−1)2 c) Var(−X−3) d) E(5X+ 4) PARTS A,B,C ARE ANSWERED ALREADY, JUST D PLEASEIf X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
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