Concepts of
Expected Value
and
Expectation
―
Illustration of the mean value
calculation
―
Illustration of the variance calculation
―
Variance shortcut formula
V(X) = E(X
2
) – [E(X)]
2

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•
Estimator – Formula or rule for estimating a
parameter value from sample data.
to estimate μ
•
An estimator is unbiased
if its expected value
equals the parameter value it estimates.
X

x
x
2
p(x)
1
E(x)
x p(x)
V(x)
E((x
E(x))
μ
=
=
⋅
=
=
−
∑
∑
2
2
2
(
( ))
( )
(
2
( )
[
( )] )
( )
x
x
x
E x
p x
x
x E x
E x
p x
=
−
⋅
=
−
⋅
+
⋅
∑
∑

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