Find the joint probability distributed function of random variables

Suppose there are n i.i.d exponential random variables,say $X_{i},i=1,2,\cdots ,n$ with probability density function $$f(x)=\left\{\begin{matrix} e^{-x} &x\geqslant 0 \\ 0& x<0 \end{matrix}\right.$$ Now let $S=\left \{ X_{i}|X_{i}<\tau ,i=1,2,\cdots ,n\right \}$ be a set of $X_{i}$s satisfying $X_{i}<\tau$.Thus,$|S|$ is a binomial random variable $|S|\sim B(n,1-e^{-\tau }).$

So what is the joint pdf of $|S|$ and all the $X_{j}\in S$,namely, the joint pdf of the size of $S$ and all the members in it?

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Really, what this is kind of saying, is, you have n radioactive atoms, each having a halflife of ln(2) second (ok, I should say decay time constant instead of half-life because there's nothing special about the number 2 when dealing with e, but just to put it in common terminology and a comprehensible situation), and of those n, |S| of them decayed within the first τ seconds. Hopefully you see that knowing how many of the n radioactive atoms in the set decayed before τ seconds pass doesn't make a lick of difference for the probability density on when any one atom decayed within that τ second period of time. Nor do they have an effect on each other. They're all still independent. It would only be if you did something like, keep the m atoms that lasted the longest among the |S| that decayed before τ seconds passed, that they would be dependent. But no, you're keeping all the atoms that decay before τ seconds pass in your set. What is the distribution just on those |S| elements? Well, that's just a simple application of Bayes's theorem. The probability of it decaying within time τ seconds is 1-$e^{-τ}$. So distribution on the |S| elements is just the original distribution divided by that over the first τ seconds, and 0 thereafter:
$f(x)=\left\{\begin{matrix} 0& 0>x\\\frac{e^{-x}}{1-e^{-τ}} &τ>x\geqslant 0 \\ 0& x\geqslantτ \end{matrix}\right.$