Question
In: Statistics and Probability
" time headway" in traffic flow is the elapsed time between the time that one car...
" 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. Suppose that in a different traffic environment, the distribution of time headway has the form
f(x)={k/x^5, x>=2
{0, x<2.
a) Determine the value of k for which f(x) is a reasonable pdf.
b) obtain the cumulative distribution function.
c) Determine the probability that headway exceeds 5 sec.
d) Find the expected value and the standard deviation of headway
Solutions
.
orchestra answered 1 year agoRelated Solutions
"Time headway" in traffic flow is the elapsed time between the time that one car finishes...
"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
x7
x > 1
0
x...
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seconds.
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Table: Insurance Claim Approval Times (days) Old Process New Process Week Elapsed Time Week Elapsed...
Table: Insurance Claim Approval Times
(days)
Old Process
New Process
Week
Elapsed Time
Week
Elapsed Time
1
31.7
13
24
2
27
14
25.8
3
33.8
15
31
4
30
16
23.5
5
32.5
17
28.5
6
33.5
18
25.6
7
38.2
19
28.7
8
37.5
20
27.4
9
29
21
28.5
10
31.3
22
25.2
11
38.6
23
24.5
12
39.3
24
23.5
Use the date in table above and answer the following questions
in the space provided...
A statistical program is recommended. A highway department is studying the relationship between traffic flow and...
A statistical program is recommended.
A highway department is studying the relationship between
traffic flow and speed. The following model has been
hypothesized:
y = β0 +
β1x + ε
where
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour.
The following data were collected during rush hour for six
highways leading out of the city.
Traffic Flow
(y)
Vehicle Speed
(x)
1,257
35
1,331
40
1,225
30
1,337
45
1,349
50
1,126...
A statistical program is recommended. A highway department is studying the relationship between traffic flow and...
A statistical program is recommended.
A highway department is studying the relationship between
traffic flow and speed. The following model has been
hypothesized:
y = β0 +
β1x + ε
where
y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour.
The following data were collected during rush hour for six
highways leading out of the city.
Traffic Flow
(y)
Vehicle Speed
(x)
1,256
35
1,328
40
1,228
30
1,337
45
1,349
50
1,122...
Traffic flow is traditionally modeled as a Poisson Distribution. A traffic engineer monitors the traffic flowing...
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A traffic engineer monitors the traffic flowing through an
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What is the random variable X described above? Write the
distribution of X using the standard notations.
What should be the variance and the standard deviation of the
number of vehicles through the intersection within a minute?
...
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