The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X ? ?with pdf a.? ketch the graph of ?f(? ? . b.? ?Find the value of ?k?. c.? ?What is the probability that the actual tracking weight is greater than the prescribed weight? d.? ?What is the probability that the actual weight is within .25 g of the prescribed weight? e.? ?What is the probability that the actual weight differs from the prescribed weight by more than .5 g?

Problem 6E Answer: Step1: We have the actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X w ith pdf We need to find, a. Sketch the graph of f(x). b. Find the value of k. c. What is the probability that the actual tracking weight is greater than the prescribed weight d. What is the probability that the actual weight is within .25 g of the prescribed weight e. What is the probability that the actual weight differs from the prescribed weight by more Than 0.5 g Step2: a). Consider, f(x) = k[1 (x 3) ], x = 2,3,4. When x = 2 When x = 3, When x = 4, b). Consider, F (x) = k [1 (x 3) ] Integrate above equation with respect to x then we get by taking limits from 0 to 2 4 4 2 P(2X 4) = f(x)dx= k[1 (x 3) ]dx 2 2 4 = k [ (x 3) ]dx 2 4 4 2 = k 1x (x 3) ]dx 2 2 3 = k [x - (x3) ]4 3 2 (43)3 (23) = k [(4 - 3 ) - (2 - 3 ) ] 11 7 = k [ 3 3 ] 4 = k 3 k = 3 4 Therefore, the value of k is 0.7500. Step3: c). 4 4 P(X >1) = f(x)x = k[1 (x 3) ]dx 2 3 3 4 2 = k [ (x 3) ]dx 3 4 4 2 = k 1x (x...