Two random variables x and y have means Ex 1 and Ey 2 vari

Two random variables x and y have means E[x] = 1 and E[y] = 2 variances Sigma^2 x =4 and sigma^2 y = 1, and a correlation coefficient psi ty = 0.4. New random variables w and v are defined by V = -x + 2y and w = x+3y. Find the mean values of v. Find the mean values of w.

Solution

(a)

v = -x + 2y

Mean value of v = - E(x) + 2E(y)

= -1 + 2*2

= -1+4

= 3 Answer

(b)

w = x + 3y

Mean value of w = E(x) + 3E(y)

= 1 + 3*2

= 1 + 6

= 7 Answer