answer all questions with detailed explanation

1) For n 2 1, Tan is a continuous random variable having pdf an (t) = 8n(1 nt)I(1/2n' 1/\") (t). (It can be noted that for all t E R, we have limn an (t) = 0, a fact which may or may not be of help to you when trying to solve this problem.) Consider the sequence T1, T 2, . . . and give the pmf or pdf of the limiting distribution. (Hint: Sketch the pdf in order to hopefully gain some insight. (What happens as n increases?))