4. "Time headway" In highway traffic flow the elapsed time between the time that one carfinishes passing a fixed point and the instant that the next car begins to pass that pointis called time headway.Now, let X = the time headway for two randomly chosen consecutive cars on ahighway during a period of heavy traffic flow. The following probability density functionof X is suggested by traffic experts:f(x) = 0.15*e-0.15(x-0.5) for (x ≥ 0.5 sec)0otherwisea. Draw f(x) from x = 0 to x= 10 sec.b. Find P(X ≤ 5 sec) and show it on the figure you have drawn.c. What is E[X] and Var[X] ?d. Find Cumulative Distribution Function of X.

Given the probability density function of the random variable X, the time headway for two randomly…

Answered: 4. "Time headway" In highway traffic…

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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Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 30 minutes (90 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) = , 70 ≤ x ≤ 110 , elsewhere
let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a client by answering phone calls, suppose that x has probability density function defin by f(x)=3x^2 for 0< x < 1. find the mean and variance of x
If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.
Suppose that the joint density function of the random variables X and Y is f(x,y)=k(1+2y), if 7<x<13 and 0<y<1, and f(x,y)=0, otherwise. Show that the marginal distribution of X is g(x)=c, if 7<x<13, and g(x)=0 otherwise. Enter the value of c. Hint: Of course, first, you need to find the value of k. Round your answer to a number with two decimal digits after the decimal point. For example if your answer is 1/40, which is equal to 0.025, then you should enter 0.03. (Do NOT use decimal comma; 0,03 would be wrong.)
The probability density function of X, the lifetime of a certain device in months, is given by f(x)=6/(x^2) if x > 6 and f(x) = 0 if x < 6. Find P(X > 50). Also, what is the cumulative distribution function of X on x > 6?
Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 40 minutes (100 minutes) to recharge the vehicle's battery. Assume that the actual recharging time required is uniformly distributed between 80 and 120 minutes. (a) Give a mathematical expression for the probability density function of battery recharging time for this scenario. f(x) = , 80 ≤ x ≤ 120 , elsewhere (b) What is the probability that the recharge time will be less than 109 minutes? (c) What is the probability that the recharge time required is at least 91 minutes? (Round your answer to four decimal places.) (d) What is the probability that the recharge time required is between 90 and 100 minutes?
Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.

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