5. (Community events, 5 points) The Lower Bay State Road neighborhoo.pdf

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5. (Community events, 5 points) The Lower Bay State Road neighborhood is organizing an egg hunt and a Bostonian brunch at Easter. Both community events start at noon. Let X be the duration of the egg hunt in minutes, and Y be the duration of the brunch in minutes. Let FX be the CDF of X, and FY be the CDF of Y . Finally, suppose X and Y are independent. Student organizer Asami stays from noon until both events are over. Let Z be the length of time she stays in minutes. For example, if X = 50 and Y = 40, then Z = 50. (a) Express Pr(Z 30) in terms of FX and FY . Resident assistant Charlotte only stays from noon until either event is over. Let W be the length of time she stays in minutes. For example, if X = 50 and Y = 40, then W = 40. (b) Express Pr(W 30) in terms of FX and FY ..

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