Example 4.5 introduced the concept of time headway intraffic flow and proposed a particular distribution for X =the headway between two randomly selected consecutivecars (sec). Suppose that in a different traffic environment,the distribution of time headway has the formx>10 x ≤ 1a. Determine the value of k for which f(x) is a legiti-mate pdf.Obtain the cumulative distribution function.b.c.f(x) =Use the cdf from (b) to determine the probability thatheadway exceeds 2 sec and also the probability thatheadway is between 2 and 3 sec.d. Obtain the mean value of headway and the standarddeviation of headway.e.What is the probability that headway is within 1 stan-dard deviation of the mean value?

Let X denotes the headway between two randomly selected consecutive cars (sec) a... Determine the…

Answered: Example 4.5 introduced the concept of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(a) Determine the value of k for a valid pdf.(b) Complete the cdf of X .(c) What is the expected total deduction on a randomly chosen form?(d) Let Y = ln(X /5), where ln(·) is natural logarithm. Determine the pdf as wellas the cdf of Y , and further identify which common distribution that Y follows?
. Find the moment generating function about origin of the Poisson distribution.
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For any number of x, the cumulative distribution function (F(x)) is the probability that the observed value of the X will be at most x. Select one: True False
In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean λ = 3. The profit per foot when the rope is sold is given by X, where X = 60 - 4Y - y². Find the expected profit per foot. $ per foot
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he chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 10-year period. Assume each year is independent. Give the distribution of X.X ~
part d please

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