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How is the following formula derived which yields the probability that the sum of the squares of n random draws from the closed interval [-1,1] is less than one?

formula: (1/2^n)*pi^(n/2)/(n/2)!

flag	asked Jun 12 2011 at 18:27 Mike Pemberton 3●1

1

I suspect Stirling's formula is involved, since $\pi$ and factorials appear. But I also suspect this is closer to being an exercise than a research question, especially since you seem sure of the formula. So this question might be more appropriate for stackexchange or maybe Wikipedia's mathematics reference desk than for mathoverflow. – Michael Hardy Jun 12 2011 at 18:56

Michael Renardy · Accepted Answer · 2011-06-12 18:59:34Z UTC

5

Volume of the ball divided by volume of the cube.

answered Jun 12 2011 at 18:59

Michael Renardy
4,771●1●10●17

Probability formula derivation

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