The sampling distribution of an estimator,
, follows a discrete distribution within the
finite population setting. Thus the expected value of
defined by equation ?? can also be
written as
 | (5.2) |
where
As an example using Table ?? where
is
, the expectation of
can also be determined
using equation ?? as in Table ??.
| Table 5.11: | Sampling Distribution of with an Unequal Probability Sampling WOR
Design. |
|
|
| | P( ) | P( ) ⋅ |
|
|
| | 45.5 | 0.003 | 0.15 |
| 50.0 | 0.010 | 0.52 |
| 50.5 | 0.017 | 0.87 |
| 51.0 | 0.007 | 0.35 |
| 52.5 | 0.018 | 0.96 |
| 53.0 | 0.018 | 0.97 |
| 55.0 | 0.020 | 1.12 |
| 55.5 | 0.041 | 2.31 |
| 57.5 | 0.057 | 3.29 |
| 58.0 | 0.037 | 2.17 |
| 58.5 | 0.030 | 1.73 |
| 59.0 | 0.030 | 1.75 |
| 60.0 | 0.064 | 3.83 |
| 60.5 | 0.042 | 2.52 |
| 62.5 | 0.111 | 6.96 |
| 63.5 | 0.092 | 5.86 |
| 64.0 | 0.060 | 3.86 |
| 66.0 | 0.161 | 10.61 |
| 68.5 | 0.179 | 12.25 |
|
|
| ∑
P( ) ⋅ | = 62.12 | =E[ ] |
|
|
| | |
|