The question below

Let X1, X2, ..., Xn be i.i.d. uniform random variables on the unit interval [0, 1]. Let Yn = min {X1, . .., Xn} and Zn = max{X1, ..., Xn}. (a) Find P(X5 > XilX1 = Z4). [5 points] (b) What is the joint pdf and the joint cdf of (Yn, Zn)? [10 points] (c) What is the probability that Yn + Zn ? [5 points]