On a lonely stretch of Interstate Highway 15 near Shelby, Montana (on the edge of the...

 

 

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On a lonely stretch of Interstate Highway 15 near Shelby, Montana (on the edge of the Western Prairie), Officer McDuane waits for cars to come by to stop them for speeding. The speed of cars is uniformly distributed from 50 to 90 miles per hour (MPH) (uniform in the interval [50, 90], continuous distribution). However, Officer McDuane only stops people whose speed X is bigger than 70 MPH. He writes each such person a speeding ticket equal to the value Y = 15+ 6X (X – 70). Remember, Office McDuane only stops a car if X > 70. In each of the questions below, select THE SINGLE correct statement. In this problem, we still consider Officer McDuane's activities, but we are no longer interested in X and Y. Therefore, this problem is independent of Problem 2. Officer McDuane estimates that his average waiting time for the next car he stops is 10 minutes, and that the waiting time T, measured in hours, is an exponential random variable. (a) The expectation of T is [5] (b) The density fr (x) of T is zero for x < 0, while for x > 0, it equals [5] (c) The probability that Officer McDuane will have to wait less than 30 minutes from the start of his shift until he stops the first car is [5] (d) Given that Officer McDuane has waited 3 hours without stopping anyone, the chance that he will have to wait at least 10 minutes more before stopping his first car is [5] (e) The total amount of time until Officer McDuane stops his 4th car is [5] (f) The standard deviation of the total amount of time until Officer McDuane stops his 4th [5] car is (g) EXTRA CREDIT (Include a written answer only, no multiple choice.) Compute the prob- ability that Officer McDuane will have to wait more than 40 minutes until he stops his 4th car. On a lonely stretch of Interstate Highway 15 near Shelby, Montana (on the edge of the Western Prairie), Officer McDuane waits for cars to come by to stop them for speeding. The speed of cars is uniformly distributed from 50 to 90 miles per hour (MPH) (uniform in the interval [50, 90], continuous distribution). However, Officer McDuane only stops people whose speed X is bigger than 70 MPH. He writes each such person a speeding ticket equal to the value Y = 15+ 6X (X – 70). Remember, Office McDuane only stops a car if X > 70. In each of the questions below, select THE SINGLE correct statement. In this problem, we still consider Officer McDuane's activities, but we are no longer interested in X and Y. Therefore, this problem is independent of Problem 2. Officer McDuane estimates that his average waiting time for the next car he stops is 10 minutes, and that the waiting time T, measured in hours, is an exponential random variable. (a) The expectation of T is [5] (b) The density fr (x) of T is zero for x < 0, while for x > 0, it equals [5] (c) The probability that Officer McDuane will have to wait less than 30 minutes from the start of his shift until he stops the first car is [5] (d) Given that Officer McDuane has waited 3 hours without stopping anyone, the chance that he will have to wait at least 10 minutes more before stopping his first car is [5] (e) The total amount of time until Officer McDuane stops his 4th car is [5] (f) The standard deviation of the total amount of time until Officer McDuane stops his 4th [5] car is (g) EXTRA CREDIT (Include a written answer only, no multiple choice.) Compute the prob- ability that Officer McDuane will have to wait more than 40 minutes until he stops his 4th car.

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Answer a Average waiting time 1a 10 minutes Rate a 1 per 10 minutes T ... View the full answer