Problem on exponential density function

Question

Response to the following problem:

Let X1, X2, X3,... denote iid random variables each uniformly distributed on [0, A], where A > 0. Let Yn = min{X1, X2,..., Xn}.

1. What is the PDF of Yn?

2. Show that if both A and n go to infinity such that n A = λ, where λ > 0 is a constant, the density function of Yn tends to an exponential density function. Specify this density function.