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The actual tracking weight of a stereo cartridge that is set to track at 9 g on a particular changer can be regarded as a continus rv X with pdf x]:{k(9[$Q}2) 6$12 0 otherwise a) Find the value of I: (give your answer as a reduced fraction) You may find it helpful to graph the function in order to answer some of the following questions. b. What is the probability that the actual tracking weight is greater than the prescribed weight? {The prescribed weight is 9 g). c. What is the probabillityr that the actual weight is within 0.3 g of the prescribed weight? |f I . (round your answer to 3 decimal places] d. What is the probability that the actual weight different from the prescribed weight by more than 0.7 g? l l (round your answer to 3 decimal places) In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 10, then it can be shown that the total waiting time Y has the pdf 1 my Uy