Probability distribution with horses

[cosmicway]

I 'm going to check what you 've done.
But did you try to verify your method using random number simulation ?
Random number simulation gives the correct answer to say one decimal place (it's drawback being that it is slow).
Another application of this one is in component failure statistics.

And hey, those numbers of yours add to 0.88801 not 1 (?)


RANDOM NUMBERS
------------------
To generate normally distributed numbers with mean zero and standard deviation 1, first generate two uniformly distributed random numbers x,y in the interval [0,1] (using the rnd function).

The normally distributed number is computed by the formula:

u = sqrt (- 2 . log(x) ) . cos ( 2 . π . y )

(π is pi, in case the Greek letter is not visible to you).

u is adjusted to mean m and standard deviation s by:

u1 = s . u + m

(source Mathematical Handbook , Abramowiz-Stegun).

Now following this procedure I run the race 10,000 times i.e. generate 6x10,000 = 60,000 u1 type numbers.

The probabilities are as follows:

horse 1: 0.47
horse 2: 0.29
horse 3: 0.19
horse 4: 0.04
horse 5: 0.01
horse 6: 0.00

(plus-minus 0.01)

The random number program was n't terribly slow but I don't like it all that much.