Acollege professor never finishes his lectures before the end of class time but always finishes within 4 minutes of the end of class time. let x denote the time that elapses between the end of class time and the actual end of the lecture. suppose also that the pdf of x is as given below. the value of k is
f(x) = kx^2 0 ? x ? 2

(a) find the value of k. (enter your answer to three decimal places.)
(b) what is the probability that the lecture ends within 1 min of the end of the hour? (enter your answer to three decimal places.)
(c) what is the probability that the lecture continues beyond the hour for between 15 and 45 sec? (round your answer to four decimal places.)
(d) what is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (round your answer to four decimal places.)