60. An exam consists of a problem section and a shortanswer section. Let X1 denote the amount of time

(hr) that a student spends on the problem section and X2 represent the amount of time the same student spends on the short-answer section. Suppose the joint pdf of these two times is

a. What is the value of c?

b. If the student spends exactly .25 hr on the shortanswer section, what is the probability that at most .60 hr was spent on the problem section?

Hint: First obtain the relevant conditional distribution.

c. What is the probability that the amount of time spent on the problem part of the exam exceeds the amount of time spent on the short-answer part by at least .5 hr?

d. Obtain the joint distribution of Y1X2/X1, the ratio of the two times, and Y2X2. Then obtain the marginal distribution of the ratio.