Question

If a, b, h, k are constants, while U and V are $U = \frac{X - a}{h},V = \frac{Y - b}{k},$ then

• A. Cov $(X,Y) =$ Cov $(U,V)$
• B. Cov $(X,Y) = hk$ Cov $(U,V)$
• C. Cov $(X,Y) = ab$ Cov $(U,V)$
• D. Cov $(U,V)$ = $hk$ Cov $(X,Y)$

Answer 1

Answer: (B)

Cov $(X,Y) = hk$ Cov $(U,V)$

Answer 2

Given that $U = \frac{X - a}{h},V = \frac{Y - b}{k}$

⇒ $X = hU + a,Y = kV + b$

$\therefore Co ⥂ v(X,Y) = hkCo ⥂ v(U,V)$,

$\lbrack\because Co ⥂ v(AX + B,CY + D) = ACCo ⥂ v(x,y)\rbrack.$