1. Let Xn denote the mean of a random sample of size n from a distribution that is . Find the Limiting distribution of Xn.

2. Let Y1 denote the first order statistic of a random sample of size n from a distribution that has the PDF . Let . Find the distribution of Zn.

1.

So to find the limiting distribution, I need to take the limit of the PDF as n approaches infinity.

Kinda stuck here.

Any help would be appreciated.