Question

So here is the problem and solution. i would like to understand how to solve the problem. Would someone please be able to link me to some specific notes/resources/videos on solving/understanding the material

thank you so much in advance!

P1. (5 pts) Y, and Y, are independent N(0,1) random variables. Let Z1 = Y, + Y , Z = Y- Y, and 23 = Y. Find Cov(2) where Z' = (21,22,23). Show your work. Solution. Note that £y = Cov (-) =(. 9) since Y, and Y, are independent N(0,1). Now, (3) - (1 :-) (%) = c (%=> Es = cx»c'= (:-)6 9G -1 °) 12 0 1 - 1 1

Answer 1

in this problem we have to find a cov (z). so , we use the basic property of covariance like independent variables are uncorrelated.

Y and 2 are independent Neal). رله لي Let Z., = Y, +Y2 Zz = Y,-₂ Zz = 12 -- - -4) - رحان لم varly) CONCY,,2) Con 12 = cover var 192 ) =0 where so coult 4 and 42 are in de bendent and vary) - var (Y) = 1. & given in questions soy Cov ( C ) 2 columns - Coult, M2) 2 - CoulY2,90 co TO fromero Con (Z) = 1 I lo ! Coul coul ) la - 1 - COUCAX) = A cou TIL OTTO 1 - 2 o 1 1-1 L1-1 C -t 2