This preview shows page 1. Sign up to view the full content.
Unformatted text preview: et , then 3. are independent.
4. The Zscore transformation of the sample mean follows the standard normal
distribution: 1 5. A Trandom variable with n1 degrees of freedom can be obtained by
replacing the population standard deviation with its sample counterpar t in
the Zscore above: *Def. of tdistribution (Student’s tdistribution, first introduced by William
Sealy Gosset )
Let
Then, , , where are independent. Wiki: William Sealy Gosset (June 13, 1876–October 16, 1937) is best known by
his pen name Student and for the Student's tdistribution.
2 *Proof of #5
We know that and Furthermore, since
are independent, thus
Therefore by the definition of tdistribution, are independent. *We will now prove #2 & #3 for the special case of n=2 (a sample of size 2).
In that case, w...
View
Full
Document
This document was uploaded on 03/15/2014 for the course AMS 412 at SUNY Stony Brook.
 Spring '14

Click to edit the document details