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 ?
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.