/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 6.14 An ambulance travels back and fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 6.14 (page 271)

An ambulance travels back and forth at a constant speed along a road of length L. At a certain moment of time, an accident occurs at a point uniformly distributed on the road. [That is, the distance of the point from one of the fixed ends of the road is uniformly distributed over (0, L).] Assuming that the ambulance鈥檚 location at the moment of the accident is also uniformly distributed, and assuming independence of the variables, compute the distribution of the distance of the ambulance from the accident.

Short Answer

Expert verified

Probability is=aL2-aL,0<a<L

Step by step solution

01

Assumption

Let X and Ydenoted respectively the locations of the ambulance and the accident of the moment the accident occurs.

02

Calculation

P(|X-Y|<a)=P(Y<X<Y+a)+P(X<Y<X+a)=2L2鈭�0L鈭�ymin(y+a,L)dxdy=2L2鈭�0L-a鈭�yy+adxdy+鈭�L-aL鈭�yLdxdy=1-L-aL+aL2(L-a)=aL2-aL,0<a<L

which is the required probability.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If X and Y are jointly continuous with joint density function fX,Y(x, y), show that X + Y is continuous with density function fX+Y(t)=q鈭�qfX,Y(x,t鈭�x)dx

Monthly sales are independent normal random variables with mean 100and standard deviation 5.

(a) Find the probability that exactly 3of the next 6months have sales greater than 100.

(b) Find the probability that the total of the sales in the next 4months is greater than 420.

Let X(1)鈥�X(2)鈥�路路路鈥�X(n) be the ordered values of n independent uniform (0,1)random variables. Prove that for 1鈥�k鈥�n+1,PX(k)鈭�X(k鈭�1)>t=(1鈭�t)n whereX(0)K0,X(n+1)Kt.

The accompanying dartboard is a square whose sides are of length 6.

The three circles are all centered at the center of the board and are of radii 1, 2, and 3, respectively. Darts landing within the circle of radius 1 score 30 points, those landing outside this circle, but within the circle of radius 2, are worth 20 points, and those landing outside the circle of radius 2, but within the circle of radius 3, are worth 10 points. Darts that do not land within the circle of radius 3 do not score any points. Assuming that each dart that you throw will, independently of what occurred on your previous throws, land on a point uniformly distributed in the square, find the probabilities of the accompanying events:

(a) You score 20 on a throw of the dart.

(b) You score at least 20 on a throw of the dart.

(c) You score 0 on a throw of the dart.

(d) The expected value of your score on a throw of the dart.

(e) Both of your first two throws score at least 10.

(f) Your total score after two throws is 30.

Let X1, X2, X3 be independent and identically distributed continuous random variables. Compute

(a) P{X1 > X2|X1 > X3};

(b) P{X1 > X2|X1 < X3};

(c) P{X1 > X2|X2 > X3};

(d) P{X1 > X2|X2 < X3}
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.