Let the continuous random variable X represent the time (in hours) it takes a student to finish an hour- long exam. Suppose X has pdf f(x) and cdf F(x). Make sure to show work for all answers below! 0 0.2 0.4 0.6 0.8 f(x) 0 0.29 0.67 1.15 1.73 F(x) 0 0.027 0.12 0.3 0.59 (a) What is F(1)? Explain. (b) Use your knowledge of F(x) and your answer to (a) to estimate f (1). (c) What proportion of students finish the exam in the last 24 minutes? (d) Let m represent the median of this distribution. Which of the following statements must be true about m? Circle your answer. (i) m = 0.5 (ii) 0.2