would you help with this stats problem? Please who the steps of how to find the answer.

A college professor never finishes their lecture before the end of the period and always finishes their lectures within 3 minutes after the period should be finished. Let X : the time that elapses between the end of the period and the end of the lecture (in minutes), and suppose that the pdf of X is: f(x) : kx2, O S x S 3, and 0 otherwise (a) Find the value of k to at least four decimal places. (Add zeroes if necessary). 1111 J (b) Find the probability the professor finishes within one minute, to within four decimal places 0370 J (c) Find the expected number of minutes that the students will not be paying attention *cough'\"... that is, the expected number of minutes that the lecture continues beyond the end of the period. _x (d) Find the Variance of the amount of time (in minutes) that the lecture continues beyond the end of the period. :I