Let-c-be-a-constant-Using-Var-X-E-X-E-X-2-show-that-a-Var-c-X-c-2-Var-X-b-Var-c-X-Var-X-

Question Number 6605 by WAI LIN last updated on 05/Jul/16

L e t c b e a c o n s t a n t . U s i n g V a r (X) = E [{(X - E [X])}^{2}], s h o w t h a t

(a) V a r (c X) = c^{2} V a r (X);

(b) V a r (c + X) = V a r (X) .

Commented by prakash jain last updated on 05/Jul/16

E (c X) = c E (X)

E (c + X) = c + E (X)

V a r (c X) = E [{(c X - c E (X))}^{2}]

= E [c^{2} {(X - E (X))}^{2}] = c^{2} E [{(X - E (X))}^{2}] = c^{2} V a r (X)

V a r (c + X) = E [{(c + X - c + E (X))}^{2}] = V a r (X)