[R] Recursive Computation in R

[Bill Venables]

> Hi there,
> 
> I want to be able to do the famous birthday problem, which will involve
> the computation of 365!, however it shall get cancelled out during the
> computation.  To make it more clear, I want to work out:
> n <- 1:80
> prob <- 1 - ( fact(365) / ( fact( 365 - n ) * 365 ^ n ) )

Rule 1: If you find yourself calculating factorials you are
probably doing it the wrong way.

Rule 2: Same for determinants, but that's another issue.

Sorry to spoil it for you, but I can't resist:

> 1 - cumprod(365:285/365)
 [1] 0.000000000 0.002739726 0.008204166 0.016355912 0.027135574
 [6] 0.040462484 0.056235703 0.074335292 0.094623834 0.116948178
[11] 0.141141378 0.167024789 0.194410275 0.223102512 0.252901320
[16] 0.283604005 0.315007665 0.346911418 0.379118526 0.411438384
[21] 0.443688335 0.475695308 0.507297234 0.538344258 0.568699704
[26] 0.598240820 0.626859282 0.654461472 0.680968537 0.706316243
[31] 0.730454634 0.753347528 0.774971854 0.795316865 0.814383239
[36] 0.832182106 0.848734008 0.864067821 0.878219664 0.891231810
[41] 0.903151611 0.914030472 0.923922856 0.932885369 0.940975899
[46] 0.948252843 0.954774403 0.960597973 0.965779609 0.970373580
[51] 0.974431993 0.978004509 0.981138113 0.983876963 0.986262289
[56] 0.988332355 0.990122459 0.991664979 0.992989448 0.994122661
[61] 0.995088799 0.995909575 0.996604387 0.997190479 0.997683107
[66] 0.998095705 0.998440043 0.998726391 0.998963666 0.999159576
[71] 0.999320753 0.999452881 0.999560806 0.999648644 0.999719878
[76] 0.999777437 0.999823779 0.999860955 0.999890668 0.999914332
[81] 0.999933109

Hmm.  Better than even chances with 23 people.  Amazing... :-)


-- 
Bill Venables,      Statistician,     CMIS Environmetrics Project
CSIRO Marine Labs, PO Box 120, Cleveland, Qld,  AUSTRALIA.   4163
Tel: +61 7 3826 7251           Email: Bill.Venables at cmis.csiro.au    
Fax: +61 7 3826 7304      http://www.cmis.csiro.au/bill.venables/



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