var-x-2-then-var-2x-3-E-x-2-then-E-2x-3-

Question Number 76726 by Rio Michael last updated on 29/Dec/19

var (x) = 2 then var (2 x - 3) = ?

E (x) = 2 then E (2 x - 3) = ?

Answered by john santu last updated on 30/Dec/19

E (x) = \sum_{x} x f (x) = 2

s o E (2 x - 3) = \sum_{x} (2 x - 3) f (x)

= 2 \sum_{x} x f (x) - \sum_{x} 3 f (x)

= 4 - 3 \sum_{x} f (x)

Commented by john santu last updated on 30/Dec/19

n o t e : \sum_{x} f (x) = 1

Answered by benjo 1/2 santuyy last updated on 30/Dec/19

u s i n g b y t h e o r e m

E (2 x - 3) = 2 E (x) - 3

s o w e g e t E (2 x - 3) = 2 \times 2 - 3 = 1

Answered by benjo 1/2 santuyy last updated on 30/Dec/19

v a r (2 x - 3) = 2^{2} v a r (x) = 4 \times 2 = 8

Commented by Rio Michael last updated on 30/Dec/19

thanks guys

Commented by john santu last updated on 30/Dec/19

y o u r w e l c o m e b r o