1. Problem 11.14 Verify that var(aX +b) = a2var(X) and cov(aX,bY) = abcov(X,Y) var(Y) (X,Y)X/ for any constants a,b. Next, evaluate the variance of

1. Problem 11.14 Verify that var(aX +b) = a2var(X) and cov(aX,bY) = abcov(X,Y)

var(Y) − ρ(X,Y)X/√

for any constants a,b. Next, evaluate the variance of the random variable Z =

Y/√

var(X) to prove that −1 ≤ ρ(X,Y) ≤ 1. Also, for anyconstantsa,b,c,andd,verifythatcov(aX + bY,cV + dW)canbeworked out as accov(X,V) + adcov(X,W) +bccov(Y,V)+bdcov(Y,W).