The following problems are from the course’s textbook: Introduction to Civil EngineeringSystems, Samuel Labi, Wiley, 2014 (ISBN: 9780470530634)):Question 1: Exercise 3, Textbook page 162.Question 2: Exercise 6 on Text page 163.Question 3.The probability that Joe is late for work is 0.20. The probability that Joe drives fast to work is 0.40. Theprobability that Joe performs well at work is 0.75. Choose 3 letters, say L, F, W, to denote each of theseevents. If Joe is late, the probability that he drives fast to work is 0.9. Assume that his punctuality orlateness to work does not influence whether he performs well at work that day. Furthermore, 30 out ofevery 100 days, he drives fast to work and does a good job in the same day. (a) For all pairedcombinations of these two events, comment on their mutual exclusivity, statistical dependence, orstatistical independence. Use the table below.PairProperty (circle one)L and FMutually exclusive/Statistically dependent/Statistically independentL and WMutually exclusive/Statistically dependent/Statistically independentF and WMutually exclusive/Statistically dependent/Statistically independent(b) Using the general probability equation and your prescriptions in (a) above, find the probability that onany randomly selected day, …(i) either he is late for work or he drives fast to work or both happen.(ii) either he is late for work or he performs well at work or both happen.(iii) either he drives fast to work or he performs well at work or both happenQuestion 4:A. Indicate which of the following random variables are discrete and which are continuous:i.Whether or not users of a civil engineering system are satisfied with the system:i.The performance of a hydraulic system in terms of volume of water pumped per hour:B. Rewrite the following stochastic events in mathematical notation using a suitably-definedrandom variable1.Of every 100 road construction projects, 28 experience two or more fatalities.ii.20% of the time, a certain aging engineering system component breaks down at least 4 timesduring operation every year.C. Write in everyday English, the stochastic events that are represented by theprobabilities of the following random variables:i.a) p(Y >7) = 0.33Y is a random variable representing the weekly number of hours workedby a randomly selected Catholic University student.ii.b) p(F 2 2) = 0.85F is a random variable representing the number of times a hydraulicsystem gets overloaded
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