申論題

11. (30%) A study show that in an exan the time required to come up with the correct answer for each question is a cont tinuous memoryless random variable with the ex expected value equal to the difficulty level of the question. The time to answer each question is independent of each other.

(b) (6%) The third question has diffieulty level 3 while the fourth question has difficulty level 5. Denote U as the random variable rep presenting the difference in time to come up with the correct answers for the two questions (time for the fourth minus time for the third). Write down the PDF of U.