Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)

[Paul Nord <paul.nord@valpo.edu>]

Craig,

It doesn’t matter for your example because pulling real numbers out of a hat is a perfect random number generator.  And for this reason, solving the problem analytically, as you have done, is better than the Montecarlo method of generating random numbers.

However, when generating random numbers with an algorithm, clipping sections out of the distribution can change the outcome.

I would bet that randperm() is careful not to make this mistake.

Paul



On Feb 26, 2014, at 1:38 PM, Craig Wiegert <wiegert@physast.uga.edu> wrote:

> It doesn't matter, aside from efficiency.
>
> If I put 6 numbers in a hat and draw two without replacement, then
> there are 30 equally likely outcomes (preserving the order of the
> numbers that are picked).
>
> Now let's say I put 6 numbers in a hat and draw two *with*
> replacement, but with the condition that if the second draw is the same
> number as the first, I put it back and redo my second draw until I get
> a different result.  Let's calculate the probability that the two
> numbers end up being "1" and "2", in that order.  Well, the first draw
> picks "1" with probability 1/6.  The second draw picks "2" 1/6 of the
> time... or "1" 1/6 of the time, in which case I redo.  That redo
> similarly picks "2" 1/6 of the time, or "1" 1/6 of the time which would
> mean *another* redo, and so on.
>
> The probability that the second draw ends up being "2" after as many
> redos as it takes is
> 1/6 (zero redos) + 1/36 (one redo) + 1/216 (two redos) + ... = 1/5.
> So the overall chance of picking "1" and then "2" is 1/30.  Aside from
> being distinct, "1" and "2" aren't special, thus all of the ordered
> pairs of distinct numbers occur with equal probability 1/30.
>
> I'm by no means proficient in matlab/octave, but it seems like all of
> this choosing code could be replaced with calls to randperm(35, 5).
>
>  - Craig