Hello tutors, can I please get you assistance with the following ?I apologize if its long, each part references the one above...

Many students never arrive to lecture on time, and always arrives within 2 min after the lecture starts. Let X be a random variable (in minutes) denoting the time thatelapses between the start of lecture at the top of the hour and the arrival of a student randomly chosen among those who arrive within 2 minutes to lecture. They tell us thatthe pdf is

()=², 0 2

()=0, otherwise ...

(a) What is k?

(b) What is the probability that a randomly chosen student arrives within 1 min after the beginning of lecture?

(c) What is the probability that the student arrives to lecture between 60 and 90 seconds after lecture starts?

(d) How might they have figured out that the density function given is the right one to model the random nature of that type of students? What does a density function measures, from the point of view of a statistician and how we mightrepresent an unusual behavior by a student.