252 a light bulb has a lifetime that is exponential

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Unformatted text preview: 400. (a) Find the mean and standard deviation for the total revenue from the tickets she writes in an hour. (b) What is the probability that between 2AM and 3AM she writes 5 tickets for speeding and 1 for DWI. (c) Let A be the event that she writes no tickets between 1AM and 1:30, and N be the number of tickets she writes between 1AM and 2AM. Which is larger P (A) or P (A|N = 5)? Don’t just answer yes or no, compute both probabilities. 2.47. Trucks and cars on highway US 421 are Poisson processes with rate 40 and 100 per hour respectively. 1/8 of the trucks and 1/10 of the cars get o↵ on exit 257 to go to the Bojangle’s in Yadkinville. (a) Find the probability that exactly 6 trucks arrive at Bojangle’s between noon and 1PM. (b) Given that there were 6 truck arrivals at Bojangle’s between noon and 1PM, what is the probability that exactly two arrived between 12:20 and 12:40? (c) Suppose that all trucks have 1 passenger while 30% of the cars have 1 passenger, 50% have 2, and 20%...
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