Problem 4 An instructor is waiting on 71 students to complete an assignment. Let X.- denote the time required for student 2' to complete the task, 2' : 1, 2, . . . .71. Suppose {X 1, X2, . . . ,Xn} is a collection of independent and identically distributed continuous random variables such that the PDF of each random variable in the collection is given by Ac'\" CL\" > 0 'L) 7 { 0 otherwise where /\\ is a constant such that A > 0. Let Xrnin denote the time that the rst completion of the assignment occurs, and let X max denote the time that the last completion occurs. 1. Construct the GDP of X max. 2. Determine the expected value of Xmax. 3. Construct the CDF of X min. 4. Determine the expected value of Xmm