Students t-distribution Derivation

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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?
 

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  • #2
Office_Shredder
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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.
 

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