Q3. (20 points) Let X be the length of time it takes Chao to grade the midterm, measured in tens of hours. The cdf of X is given by f(x) |= { 1- 1- (16/x4) if x 2 0 if x 2 (a) (5 points) Find the probability density function for X; be explicit about all cases. (b) (7 points) How long does Joe expect to take grading the midterm? (c) (8 points) It is now 7:00am and Chao has been grading nonstop for 2 full days (night and day). What is the probability that Chao is done grading in time to hand the midterms back at 12:50pm today?