"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 consecuti 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. x> 1 f(x) =10 (a) Determine the value of k for which f(x) is a legitimate pdf. 9 (b) Obtain the cumulative distribution function. x > 1 F(x) = xS1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)

"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 consecuti 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. x> 1 f(x) =10 (a) Determine the value of k for which f(x) is a legitimate pdf. 9 (b) Obtain the cumulative distribution function. x > 1 F(x) = xS1 (c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)

Name: Need help with unanswered sections "Time headway" in traffic flow is t
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Need help with unanswered sections "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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

See similar textbooks

Similar questions

Let X1, X2,...X100 be the annual average temperature in Paris in the years 2001, 2002, ..., 2100, respectively. Assume that average annual temperatures are sampled i.id. from a continuous distribution.(Note: For this problem, we assume the temperature distribution doesn't change over time. With global warming, this is not a good assumption.)A year is a record high if its average temperature is greater than those in all previous years (starting with 2001), and a record low if its average temperature islower than those in all previous years. By definition, the year 2001 is both a record high and a record low.1. In the 20 century (the years 2001 through 2100, inclusive), find the expected number of years that are either a record high or a record low.2. Let N be an r.v. representing the number of years required to get a new record high after the year 2001. Find P(N > n) for all positive integers n, and use thisto find the PMF of N.3. Check answers to parts (1) and (2).4. Explain how…
The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and it’s Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following : a. E(x) b. P(x=1) c. P(x=4) d. P(x6) e. P(2x5)
Two pilots (X and Y) are assigned to a flight from Atlanta to Chicago. Both need to be in the airport by 9pm, otherwise the flight will be delayed. Earlier in the day, X flies from Cedar Rapids and is scheduled to land at 8:30pm. Y arrives from Minneapolis and is scheduled to land at 8:30pm as well. Both flights are running late, and the delays are well modeled by exponential distribution with averages 20 minutes for the flight from Cedar Rapids and 15 minutes for the flight from Minneapolis. In detail please solve the following:i. Find probability that X lands by 9pm.ii. Find probability that flight to Chicago will have to be delayed.iii. Suppose that you have another pilot who could be assigned to Chicago flight, so you only need either X or Y. Find probability that flight to Chicago will depart on time.
The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.
If X has the discrete uniform distribution f(x) = 1k for x = 1, 2, ... , k, show that(a) its mean is μ = k + 12 ;(b) its variance is σ2 = k2 − 112
Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γ E[I], where γ >1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1. [Hint: draw a coordinate plane with p on the x-axis and M on the y-axis.] Based on this graph, under what conditions is she least likely to buy the subsidized insurance?
If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by M(x1, x3) = F(x1, q, x3) for −q < x1 < q, −q < x3 < q and that the marginal distribution function of X1 is given by G(x1) = F(x1, q, q) for −q < x1 < q With reference to Example 19, use these results to find (a) the joint marginal distribution function of X1 and X3; (b) the marginal distribution function of X1.
Consider a stable single-station queue. Suppose it costs $c to hold a customer in the system for one unit of time. Show that the long-run holding cost rate is given by cL, where L is the mean number of customers in steady state.
LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.
If X is a random variable with expectation µ and variance cµ2 , where c is a constant. Find a variance stabilizing transformation of X.
Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.
Let X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution of the sample maximum X(n)