• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Statistics wikipedia, lookup

History of statistics wikipedia, lookup

Transcript
```Random Sampling
Population
 Random sample:



Independent variables
Same probability distribution
Statistics
 Point estimate

1
Examples
Mean  of a single population
2
 Variance  of a single population
 Difference in means of two population

1   2
2
Unbiasedness
An estimator  of some unknown
quantity  is said to be unbiased if the
procedure that yields  has the
property that, were it used repeatedly
the long-term average of these
estimates would be .
 That is to say, E() = .

3
Example 1
Given X = (5.8, 4.4, 8.7, 7.6, 3.1)
 The Sample Mean X
~
 The Sample Median X
 The 20% trimmed mean Xtr ( 20)

4
Example 2

Sample Variance
n
S2 

2
(
X

X
)
 i
i 1
n 1
Expectation of Sample Variance
E(S )  
2
2
5
Variance of a Point Estimator
MVUE – Smallest variance estimator
 Theorem

If X1,…Xn is a random sample of size n
form a normal distribution with mean 
2
and variance  , then the sample mean X
is the MVUE for 
6
Example 1
V( X)  
(continued)
2
n
~
2
V ( X)  
V( Xtr ( 20) )  
2
0.6n
7
```
Related documents