'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 be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?
'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 be the time headway for two randomly chosen consecutive cars (in seconds). Suppose X has pdf f(x) {* F(x) (a) Find the value of k. (b) Obtain the mean value of headway and the standard deviation of headway. (c) The cdf of X is = x > 1 x ≤ 1 0 1- x ≤ 1 x>1 Using the cdf, determine the following probabilities. (i) What is the probability that observed depth is at most 3? (ii) What is the probability that observed depth is between 3 and 2?
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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!['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 be the time headway for two randomly chosen
consecutive cars (in seconds). Suppose X has pdf
f(x)
=
{*
F(x)
(a) Find the value of k.
(b) Obtain the mean value of headway and the standard deviation of headway.
(c) The cdf of X is
=
x > 1
x ≤ 1
0
1-
x ≤ 1
x>1
Using the cdf, determine the following probabilities.
(i) What is the probability that observed depth is at most 3?
(ii) What is the probability that observed depth is between 3 and 2?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67540c0c-0996-4e08-9c56-e8b7c18daa2d%2F406fbf8d-66f3-4c9c-bc9e-b91225784d60%2Ffg2ambc_processed.jpeg&w=3840&q=75)
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 be the time headway for two randomly chosen
consecutive cars (in seconds). Suppose X has pdf
f(x)
=
{*
F(x)
(a) Find the value of k.
(b) Obtain the mean value of headway and the standard deviation of headway.
(c) The cdf of X is
=
x > 1
x ≤ 1
0
1-
x ≤ 1
x>1
Using the cdf, determine the following probabilities.
(i) What is the probability that observed depth is at most 3?
(ii) What is the probability that observed depth is between 3 and 2?
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