"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant
that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.f(x) = k/(x^7) ; x > 1 0 ; x<1a) Determine the value of K for which f(x) is a legitimate pdfb) Obtain the cumulative distribution functionF(x) = [ Blank ] ; x > 1 0 ; x < 1c) Use the cdf from (b) to determine the probability that headway exceeds 2 sex. (Round your answer to three decimal places.)Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec (round your answer to three decimal places)d) Obtain the mean value of headway and the standard deviation of headway. (Roun to nearest 3 decimal places)mean [ blank ]standard deviation [ blank ]e) what is the probability that headway is within 1 standard deviation of the mean value
1 answer:
You might be interested in
Answer:
d = 48t will represent the distance 'd' traveled in 't' hours.
Step-by-step explanation:
Jason leaves Detroit at 2:00 PM and passes through Ann Arbor at 2:50 PM which is 40 mi distant from Detroit.
Speed during this journey was constant.
Jason traveled 40 mi in 50 minutes or hours from Detroit to Ann Arbor.
By the formula,
Speed =
Speed =
= 48 mi per hour
If he travels 'd' miles in 't' hours then by the formula of speed,
48 =
d = 48t