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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2. Consider the experiment of rolling a die until a "6" appears. Let X be the number of rolls needed. Plot the Cumulative distribution function Fx(x) of X. Describe what it means for a function to be right-continuous. You are encouraged to use a computer program to plot this, although it is acceptable that you use rulers and pencils. (You don't need to plot the whole function because the possible values could be ar- bitrary large. Try to plot from 0 to the value that you think it shows the major trend.)
1. or a cumulative distribution funetion (cdf). Decide if the function graphed below is a probability density function (pdf) 2c 4 8.
The (cumulative) distribution function of X is given below: for Fx(x) = ¹ for { for (a) Determine the pdf for X. (b) Determine the value of the constant k. x 1.
Suppose that the lifetime in years, X, of a type of electrical switch follows the distribution f(x)=12e−x2f(x)=12e−x2for x>0x>0. What type of continuous distribution is this and what is the average lifetime of one of these switches?
(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.
A drawer holds purple socks and yellow socks. If n socks are taken out of the drawer at random, the probability that all are yellow is 1/2. What is the smallest possible number of socks in the drawer (as a function of n)?
Students arrive one at a time, completely at random, to an advice clinic at a rate of10 per hour. Students take on average 5 minutes of advice but there is wide variation inthe time they need; this variation may be well modeled by the exponential distribution.b. Again assuming one advisor, what is the probability that there are more than tenstudents in the clinic at a random point in time? What is the probability that the timespent in the clinic exceeds 30 minutes?.
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
if x 20 Find the following: P(X > 22) =| The cumulative distribution function of X: if x 20 The probability that at least one out of 8 devices of this type will function for at least 29 months:
If the iron cutting machine in a factory works continuously for a certain period of time under the same conditions, it goes into malfunction. In this type of failure, the machine takes 24 hours to cool down. After the machine has cooled down, it continues to work the next day. Assume that the running time (minutes) of this machine until it malfunctions has a normal distribution. The working time of the iron cutting machine until the failure was measured for 9 different days, which were chosen at random. Continuous working time (minutes): 14-26-18-29-12-19-22-30-19 a) Establish the 95% confidence interval for the average uninterrupted working time of this iron cutting machine and interpret the result.b) The factory chief claims that the average continuous operating time of the machine is less than 23 minutes. Test the claim that the average continuous working time of this iron cutting machine is less than 23 minutes at the 0.05 significance level and the result isPlease comment.
part d please

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