It was given that a random variable T is said to have a tn distribution when:

but while proving for the density function (pdf) of a tn distribution, why is is equal to the joint distribution ?

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- August 21st 2009, 10:52 PMnoob mathematiciant distribution
It was given that a random variable T is said to have a tn distribution when:

but while proving for the density function (pdf) of a tn distribution, why is is equal to the joint distribution ? - August 21st 2009, 10:59 PMmatheagle
You first find the joint denisty of Z and U, where you needed to say that

and (and they are indep.)

Then pick a dummy varable, say W=Z or W=U.

(IF you let W=U, then you can do this, but you better check your bounds of integration.)

Use calc3 to find the density of T and W.

THEN integrate out the W and you have the density of U. - August 21st 2009, 11:36 PMnoob mathematician
Well initially I was trying to solve it by 1st letting:

then follow by:

but it turned out to be very complicated - August 22nd 2009, 06:26 AMmatheagle
this is in many books

I bet you can find it online too.

I did a quick search yesterday, but didn't find it.

I have it some where in my office and I know I can do it,

but I don't have the time.

It's in Hogg and Craig.