Students t-distribution Derivation

  • Thread starter taper100
  • Start date
  • #1
7
0

Main Question or Discussion Point

I have attempted a derivation of the Students t-distribution probability distribution function in the attached pdf. I defined T to be Z/sqrt(W/v) where Z has standard normal distrubution and W has chi squared distribution with v degrees of freedom. I know that Z and W need to be independent, but I did not use this fact in my derivation. Can someone tell me where I went wrong in the derivation or where I unknowing used this fact in my derivation?
 

Attachments

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
3,750
99
On the first line,
[tex] P(T\leq t | W = w) = P(\frac{Z}{c} \leq t ) [/tex]
assumes that Z and W are independent already, since you're saying that the probability that Z is smaller than some number is independent of what our measurement of W is.
 

Related Threads on Students t-distribution Derivation

Replies
2
Views
61K
Replies
1
Views
6K
  • Last Post
Replies
2
Views
2K
Replies
5
Views
781
  • Last Post
Replies
5
Views
15K
  • Last Post
Replies
1
Views
11K
  • Last Post
Replies
10
Views
8K
  • Last Post
Replies
0
Views
979
Top