, p(xn) respectively Let μ = E (X) be the mean of X The variance of X, denoted by Var (X) or 
2
 x
 is
defined as
2
σx
 =
2
1
Var(X)=
(
μ)
(
)
n
i
i
i
x
p x
=
−
∑
or equivalently
2
 x
 = E(X – μ)2
O
1 8
2 8
3 8
P(Y)
O
1 8
2 8
3 8
P(X)
1
2
3
4
1
2
3
4
–1
5
6
(i)
(ii)
© NCERT
not to be republished
PROBABILITY      567
The non-negative number
σx =
2
1
Var(X) =
(
μ)
(
)
n
i
i
i
x
p x
=
−
∑
is called the standard deviation of the  random variable X Another formula to find the variance of a random variable