Buffon''s needle problem, Advanced Statistics

Buffon's needle problem: A problem proposed and solved by the scientist Comte de Buffon in 1777 which includes determining the probability, p, which a needle of length l will intersect the line when thrown at the random onto a horizontal plane which  is ruled with the parallel lines a distance a > l apart. The solution can be given as


323_buffens needle problem.png 

It can be used to evaluate the p since if the needle is tossed N number of times independently and yi = 1 if it intersects the line on the ith toss and 0 otherwise then the condition becomes

1115_buffens needle problem1.png 

In the year 1850 R.Wolf (who is an astronomer in Zurich) threw the needle 5000 times and obtained the value 3.1596 for the p.

 

 

Posted Date: 7/26/2012 5:44:06 AM | Location : United States







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