Page 150 - Math Grade 12 (Advance)

PROEUS DARA

2
2. ~tl~1ri~Hi E(X )
u lju
2
E(X ) = Li P(X = x)

= 1(0.1)+4(0.3)+9(0.2)+16(0.3)+25(0.1) = 10.4
2 2 2
r~ms Var(X) = E(X ) -11 = 10.4-3 = 1.4

!:jtHsg Var(X) = 1.4 '1
u

l. Var(a) = 0 ttlru a r:hUSStG~
u
2
2. Var(aX) = a Var(X)
2
3. Var(aX+b) = a Var(X) ttlru a ~h b r:hG~StG~ '1
MlJ:fl t!J'U f{/1 fi :

2 2 2
1. Var(a) = E(i)- E (a) = a - [E(a)]
2 2
= a -a = 0 tt11 ru E(a) = a '1

2 2 2 2 2 2
2. Var(aX) = E(a X )-E (aX) = a E(X )-[E(aX)]
2 2 2 2 2 2 2 2
= iE(X )-[aE(X)] = a E(X )-a E (X) = i[E(X )-E (X)]

2
=a Var(X) '1
2
3. Var(aX +b) = E(aX + b/- E (aX +b)
2 2 2 2
=E(aX +2abX+b)-[E(aX+b)]
2 2 2 2
= a E(X ) + 2abE(X) + b - [aE(X) + b]
2 2 2 2 2 2
= a E(X ) + 2abE(X) + b - a E (X)- 2abE(X)- b
2 2 2 2 2 2
= a E(X )-a E (X) = i[E(X )-E (X)]
2
= a Var(X) '1

145