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Unformatted text preview: et , then 3. are independent.
4. The Z-score transformation of the sample mean follows the standard normal
distribution: 1 5. A T-random variable with n-1 degrees of freedom can be obtained by
replacing the population standard deviation with its sample counterpar t in
the Z-score above: *Def. of t-distribution (Student’s t-distribution, first introduced by William
Sealy Gosset )
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 t-distribution.
2 *Proof of #5
We know that and Furthermore, since
are independent, thus
Therefore by the definition of t-distribution, are independent. *We will now prove #2 & #3 for the special case of n=2 (a sample of size 2).
In that case, w...
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This document was uploaded on 03/15/2014 for the course AMS 412 at SUNY Stony Brook.
- Spring '14