CS714/814 Fall 2013
Assignment 1 Buffon’s Needle
Due on: Sept. 18, 2013.
Total points: 100
1. Brain Part: (50 pts)
In Buffon’s Needle problem, assume that the distance between lines is d and the length of the needle is l (l<=d). The total number of drops is N and the number of hits is n. Prove that
PI»2Nl/nd
(hint: deduce the probably of a needle hits a line)
2. Computer Part: (50 pts)
Write a computer program to simulate the Buffon’s needle specified in part 1. You can set both l = d = 1. Plot the variance of the PI value you obtain for 10, 100, 1000, …, 106 independent experiments. What conclusion can you get? You can use any programming language you want. Notice that the variance for a binomial distribution is P*(1-P)/N.
Delivery
form
The delivery form of the assignment should be a document with
the proof, program printout, and the corresponding graphs.