Re: Random numbers

On Mon, 24 Dec 2007 00:10:57 -0500, quasi <quasi@xxxxxxxx> wrote:

On Sun, 23 Dec 2007 19:46:21 -0800 (PST), bill <b92057@xxxxxxxxx>
wrote:

On Dec 22, 5:25 pm, quasi <qu...@xxxxxxxx> wrote:
On Sat, 22 Dec 2007 16:30:20 -0800 (PST), bill <b92...@xxxxxxxxx>
wrote:

On Dec 22, 10:16 am, quasi <qu...@xxxxxxxx> wrote:
On Fri, 21 Dec 2007 10:57:00 -0800 (PST), simple.pop...@xxxxxxxxx
wrote:

On Dec 21, 11:37 pm, bill <b92...@xxxxxxxxx> wrote:
On Dec 21, 3:16 am, John <iamach...@xxxxxxxxx> wrote:

Given a function that returns a random number between 1-5, write one
that returns a random number between 1-7 for the case when it should
be integer and for the case it can be real.

Let S be the function that generates a RN between 1 and 5. Then

T = S_1 + S_2 + ... + S_7

For the reals , RN_7 = T/7

May be this should fix it:

For the reals , RN_7 = 1 + (T-7)*3/14

Yes, that fixes the range.

But it's still biased (that is, not a unform distribution).

quasi

The OP does not specify a uniform
distribution, merely the range.

This has already been discussed.

The obvious assumption _implicit_ in the problem, even if not unstated
is that the resulting distribution should be uniform. Of course, it
should have been specified, but common sense dictates that in the
absence of the required info, to choose the natural default.

If there was no preference for a distribution, there would be no need
to use the RNG provided for the range 1 to 5. We could just always
produce the number 3, for example. In other words, the very fact that
an RNG for the range 1 to 5 was given as part of the problem makes it
clear that the for the actual problem (not the OP's deficient
statement of it), it almost certainly _was_ specified that the
required distribution should be uniform.

RN_7 = T/7 satisfies the range 1 thru 7.

So what? It's badly biased. Worse, since there is no discussion of
bias or the lack of it, it's misleading to those unaware of the issue.

T/7 is a numner in the range 1 thru 7,
but is it random?

Ok, but note that T/7 never exceeds 5.

It's definitely not uniformly random.

If RN_7 = T mod 7 +1, the probability
of a correct guess is 1/7

Nonsense. Do a simulation.

Ok, for the above, I must apologize. For the _integer_ case, the
calculation (T mod 7) + 1 does appear to give a uniform distribution

Hehe -- I take back part of my apology. It _is_ biased, but only
slightly.

The probabilities for y = (T mod 7) + 1 are as follows:

P(y=1) = .1430656
P(y=2) = .1430016
P(y=3) = .1428224
P(y=4) = .1426432
P(y=5) = .1426432
P(y=6) = .1428224
P(y=7) = .1430016

The above probabilities are exact, hence you can see a slight bias. Of
course, while I had originally intuited a bias, I expected it to be
badly biased. I was wrong about that. Only the continuous case is
badly biased.

quasi
.

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