Let X and Y be random variables with SDX sigmaX 5 SDY sig

Let X and Y be random variables with SD(X) = sigmaX = 5, SD(Y) = sigmaY = 7, SD(3X + 4Y) = 27. Find Coff(X, Y) = p.

var(3X+4Y) = 27^2 = 729

var(3X+4Y) = Var(3X) + var(4Y) + 2 * COV(X,Y) = 729

9 Var(X) + 16 Var(Y) + 2 * COV(X,Y) = 729

9 * 5^2 + 16 * 7^2 + 2 * COV(X,Y) = 729

COV(X,Y) = -140

Corr(X,Y) = COV(X,Y)/sd(X) sd(Y)

= -140/5*7

= -4