please provide detailed solution with explanation and justification for each part asap to get a upvote

2. [15 marks] We consider a sequence of random variables X1, X2, ... consisting of independent exponential random variables with rate 1. We let m 2 0, and define the random variable M by M = min {n : X. > m). (a) [5 marks] What is the PMF of M? (b) [5 marks) What is the PDF of Xar? (c) [5 marks] Is Af independent of XM