Exercise 1.3. It can be shown that the probability density function of Sn is given by fsn (20) = In (n - 1)! on-le-Xx x 2 0 (1) Using this density function, show that the probability density function of Yn is nn -1/2 n-1 fyn (y) = (n - 1)! 1 exp y > - vn (2) HINT: First, write In as a function of Sn. Then, use this function to determine both (a) the set of possible outcomes for Yn based on the set of potential outcomes for Sn, and (b) the probability density function of Yn over these outcomes, based on the probability density function of Sn.]