Re: Random numbers

On Dec 22, 10:43 am, vr <simple.pop...@xxxxxxxxx> wrote:
On Dec 22, 11:35 pm, quasi <qu...@xxxxxxxx> wrote:



On Sat, 22 Dec 2007 10:32:37 -0800 (PST), vr <simple.pop...@xxxxxxxxx>
wrote:

On Dec 22, 11:16 pm, 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- Hide quoted text -

- Show quoted text -

Hmm. Let me simplify it:

RN_7 = T*3/14 - 0.5

If you look at T*3/14, it just scales the sum of random numbers
uniformly using a constant multiplier. Did I miss to notice any non-
uniformity here?

Yes, T is not uniformly distributed in its range.

Ok. But if S_n is guaranted to be uniformly distributed in the range 1
to 5, then doesn't it mean the sum of 7 such numbers will also get
distributed over 7 to 35? I'm just curious. Thanks.

The sum is not uniformly distributed over the integers from 7 to 35.
Imagine for example tossing two fair dice. We are familiar with the
fact that the sum is not uniformly distributed over the integers from
2 to 12: a sum of 2 is much less likely than a sum of 7.

In general, let n be a fixed positive integer, and let T_1, T_2, ...,
T_n be independent reandom variables, each uniformly distributed oover
the integers from 1 to 5. Let f be any function of n variables, and
let X = f(T_1, T_2, ..., T_n). Then X cannot be uniformly distributed
over the integers from 1 to 7. So any algorithm to produce a random
variable uniformly distributed over the integers from 1 to 7 from
independent random variables uniformly distributed over the integers
from 1 to 5 must use a "variable" n. Some of the algorithms that have
been proposed above do indeed use such a variable n, and work.
.

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