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
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F781395ef-5933-4a4d-9640-3099b49e30d5%2Fbd50e136-31aa-42f2-a953-35af0ada31dd%2Fs97r0ba_processed.png&w=3840&q=75)
!["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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F781395ef-5933-4a4d-9640-3099b49e30d5%2Fbd50e136-31aa-42f2-a953-35af0ada31dd%2Fmar9w2i_processed.png&w=3840&q=75)
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