Question

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(4pt) The variance of random variable x is 1 and the variance of random variable Y is 16. The correlation coefficient between the two random variables X and Y is 0.9. (a) (1pt) Find the covariance between X and Y. (b) A new random variable Z is given by Z = 5x + 1. Find the covariance between X and Z. (1 pt) Find the covariance between Y and Z. (2pt)

Answer 1

Question Vas (x)=1; vas ()-16; 1 - 2xy = 013, (a)- sunce, Exil Auswer Cor(x,y) Svar (x) Jvar (1) thus, cor (x, y) = {x,y: Svar(x) :Ivas, (y) = (0.9)5 NG = (0.3)(4) Cor(x, y) = 3.6 (b) Com (X,Z) = Cov (X, 5x+1) = Cow (X, 5X) + Cov (x,1) - Cov (7,5x) +0 5. Cor (x,x) = 5. Var (X) = 5.0/) = 5 Thus, Cor (X, Z) = 5 answer Corry, z) = cov (4, 5x+1)= Cov (4, 5x)+ Cov (4,1) - Cow (, 5x) + O = 5. Cov(x, y) = 5 (36) = 10 Thus, Corry, z) = 18 Answer