1
Random Sampling
!
Population
!
Random sample:
!
Independent variables
!
Same probability distribution
!
Statistics
!
Point estimate
2
Examples
!
Mean
of a single population
!
Variance
of a single population
!
Difference in means of two population
µ
2
σ
2
1
µ
−
µ

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3
Unbiasedness
!
An estimator
Θ
of some unknown
quantity
θ
is said to be unbiased
if the
procedure that yields
Θ
has the
property that, were it used repeatedly
the long-term average of these
estimates would be
θ
.
!
That is to say, E(
Θ
) =
θ
.
4
Example 1
!
Given X = (5.8, 4.4, 8.7, 7.6, 3.1)
!
The Sample Mean
!
The Sample Median

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