Suppose X follows a uniform distribution on (0, 1).

(a) What is the distribution of Y = -log X?

(b) What is the expected value of Y?

(c) Suppose there are 5 students in a class taking the same exam and it takes the ith student Y_i hours to finish the exam, for i= 1,....., 5 , where Y₁,....., Y₅ are independent and identically distributed according to the distribution you found in part (a). All students start to work on the exam at the same time, and each student takes as long as theyneed to finish the exam (with no upper bound in time). What is the probability thatall five students finish the exam inone hour or less?