All parts required, thank you!

Jim the statistics student is woken at 3 AM each morning by his mother. He then lies in bed for up to 2 hours. Upon rising, it takes Jim an hour to shower and have breakfast. After that, Jim likes to watch the videos he never got around to the night before. He is however very disciplined, and never leaves home for the ANU later than noon. Although disciplined, Jim is certainly not rigid in his habits, and it wouhl be impossible to claim that there is a time (or rather interval of time) from 8 AM to 10 AM at (in) which he is more or less likely to get up than any other (interval of the same length). Similarly, than the time he has had breakfast and showered to noon, more is no particular time at which Jim is more or less likely to leave the house than any other. Let X be the time in hours that Jim lay in bed yesterday (after waking at 3 AM), and let Ybe the number of hours om waking to the moment he left home. Find and sketch (where indicated}: (a) for). the marginal pdf'othsketeh} (b) f(y l x). the conditional pdf of 1" givenX = x (sketch) (e) fix,y) . thejoint pdf of'X and 1" (sketch in 2 dimensions} (d) fly), the marginal pdf of l" (sketch) (2) x I 2) , the conditional pdfofx given 1" = 2 {sketch} m HX>U2|Y=2L the probability that Jim lay inhed past 8.30 AM yesterday. given that he left home at It.) AM (at E(X|}'=2) (It) the probability that Jim was up at 8.30 AM yesterday. given that he was not at home when you dropped in on him at It) AM in E(X|}'