A patient visiting a medical clinic spends part of their time in the waiting room and part of their time in an examination room. Let X the proportion of the total time at the clinic that the patient in the waiting room and suppose that X has pdf given by

f(x) = cx(1 – x ² ) for 0 < x < 1

f(x) = 0 otherwise.

In this situation, the expectation X =

a. 8/15

b. ¼

c. 1/5

d. 2/3

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