Question: * 12. BuffonLaplace needle. Let a, b > 0. The Cartesian plane is ruled with two sets of parallel lines of the form x =

* 12. Buffon–Laplace needle. Let

a, b > 0. The Cartesian plane is ruled with two sets of parallel lines of the form x = ma and y = nb for integers m and n. A needle of length ℓ (< min{a, b})

is dropped at random. Show that the probability it intersects some line is ℓ(2a+2b−ℓ)/(πab).

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Elementary Probability For Applications Questions!

Answer and solve the following questions. A. B. 16. What is asked in the problem? A. The length of time it takes Lianne to wash her clothes B. The work done by Lianne. C. The time Lianne washed her...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

1. (1 point) 3. (1 point) (Note: This problem is similar to problem 6 in section 1.1 of your textbook.) (Note: This problem is similar to problems 1-3 in section 1.1 of your text.) Let U = {3, 4, 6,...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

5 page2.jpg" />9 page6.jpg" />5 page1.jpg" />5 page2.jpg" />6 page2.jpg" />5 page1.jpg" />9 page6.jpg" />9 page5.jpg" />9 page5.jpg" />9 page4.jpg" />9 page3.jpg" />8 page3.jpg" />8 page2.jpg" />8...

answer all questions promptly What is the maximum segment length of a 100Base-FX netdwork,Thelast character('X', etc) refers to the line code method used. Line code is a pattern of voltage, current...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

This question involves the use of AGGREGATE linear PYTHOIN regression on the Auto data set. (a) Perform a simple linear regression with mpg as the response and horsepower as the predictor. Describe...

networsksss [4 marks] (c) Write down a HOPLA term realising the parallel composition of PCCS. Use this to give an encoding of PCCS into HOPLA, specifying a HOPLA term JPK for every PCCS term P....

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

(a) Show that Eq. (34.6) can be written as s' = sf /(s f) and hence that the lateral magnification, given by Eq. (34.7), can be expressed as m = f / (f s). (b) Use these formulas for s' and m to...

Do social networks bridge the cultural divide between countries?

When an interim period is treated as an integral portion of an entire year, bonuses paid to key employees in December are recognized as expense Multiple choice question. in total in the fourth...

Based on Exhibit 9-9 , what would be the monthly mortgage payments for each of the following situations? a. $40,000, 15-year loan at 5.5 percent. b. $76,000, 30-year loan at 6 percent. c. $65,000,...