Hi, I am very confused by this question, even though I got the answers, please help me explain all these four questions step by step, Thank you so much!

Question 3 Suppose the number of hours that Dirk works productively on any given day is uniformly distributed between 0 and 2.4 hours. Assume the number of hours that Dirk works productively is independent from day to day. a) b) d) If Dirk worked productively for more than an hour today, nd the probability that Dirk worked productively for less than 1.62 hours. Solution: 0.4429 Over the next 2 days, nd the probability that the most amount bf time Dirk worked productively on a day was more than 1.62 hours. Solution: 0.5444 Dirk wants to get a good start to the upcoming 5-day week (Mon - Fri), so on both Monday and Tuesday, Dirk plans to work productively for twice aslgngas he normally would on any given day. Find the variance of the total number of hours that Dirk works productively over the upcoming 5-day week (Mon - Fri). Solution: 5.28 hours2 Dirk's excuse for drinking lots of coffee is that it helps him be more productive at work. Suppose now that the number of hours that Dirk works productively on any given day is uniformly distributed between 0 and X hours, where X is the number of cups of coffee Dirk drinks on that day. Find the probability that Dirk works productively for more than 1.62 hours today. The joint probability distribution of X and Y given in Question 1 is displayed again below: y (Biscuit) 3 4 6 0.12 0.25 0.04 0.14 0.20 0.02 0.10 0.05 0.08 x (Coffee) \"4050.: Solution: 0.6282