consecutive cars on a freeway during period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form. f(x) - x > 1 xs1 (a) Determine the value of k for which f(x) is a legitimate pdf. 11 (b) Obtain the cumulative distribution function. 1 F(x) = x > 1 xs1

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Chapter1: Combinatorial Analysis
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Please help with part g, d, and e

last name
first name
ticket id
email
status
password
phone_number
ticket status
address
username
customer
Payment
flight_number
departure
destination
password
username
departure_time
Booked flight
flight
arrival time
price
administrator
Scheduled
Is Belong to
airline
Modified
airline_logo_path
airline_name
Transcribed Image Text:last name first name ticket id email status password phone_number ticket status address username customer Payment flight_number departure destination password username departure_time Booked flight flight arrival time price administrator Scheduled Is Belong to airline Modified airline_logo_path airline_name
"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.
k
x > 1
f(x) =
12
x < 1
(a) Determine the value of k for which f(x) is a legitimate pdf.
11
(b) Obtain the cumulative distribution function.
1
x > 1
F(x)
%3D
X< 1
(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.)
0.0005
Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)
0.0005
(d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.)
mean
standard deviation
(e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)
Transcribed Image Text:"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. k x > 1 f(x) = 12 x < 1 (a) Determine the value of k for which f(x) is a legitimate pdf. 11 (b) Obtain the cumulative distribution function. 1 x > 1 F(x) %3D X< 1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean standard deviation (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)
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