Suppose a professor never finishes his lecture before the end of the hour but always finishes within 4 minutes after the end of the hour. Let X = (elapsed time between end of hour and end of lecture) have the following probability density function: f(x) = k x2 for (0 ? X ? 4) with f(x) = 0 otherwise.
a.) Determine the value of k. (Give decimal answer to three places past decimal.)
b.) What is the probability the lecture ends within 2.5 minutes of the end of the hour(Give decimal answer to three places past decimal.)
c.) What is the probability the lecture ends between 2.0 and 4.0 minutes after the end of the hour? (Give decimal answer to three places past decimal.)
