[R] monte carlo method for circle area

[(Ted Harding)]

On 31-Mar-03 Douglas Bates wrote:
> Interestingly, in my first simulation I got a ratio that is exactly
> pi/4 to 4 significant digits.
> 
>> rdat = matrix(runif(10000 * 2, min = -1 , max = 1), nrow = 2)
>> sum(colSums(rdat * rdat) < 1) 
> [1] 7854
>> pi/4 
> [1] 0.7853982

Assuming your error e <= 0.00005 (taken literally, e = 0.0000018).

s = SD = sqrt(p*(1-p)/10000) = 0.004105458 where p = pi/4.

So your e <= 0.00005/s SDs = 0.01217891 SDs, and

P = pnorm(0.01217891) - pnorm(-0.01217891) = 0.009717124

so you are significant! (Not that that's news).

(with e = 0.0000018, we get P = 0.0003498250, but let's not exaggerate)

Cheers,
Ted.


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Date: 31-Mar-03                                       Time: 22:07:36
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