quasi
Posts:
12,067
Registered:
7/15/05


Re: Random numbers
Posted:
Dec 22, 2007 8:25 PM


On Sat, 22 Dec 2007 16:30:20 0800 (PST), bill <b92057@yahoo.com> wrote:
>On Dec 22, 10:16 am, quasi <qu...@null.set> wrote: >> On Fri, 21 Dec 2007 10:57:00 0800 (PST), simple.pop...@gmail.com >> wrote: >> >> >> >> >On Dec 21, 11:37 pm, bill <b92...@yahoo.com> wrote: >> >> On Dec 21, 3:16 am, John <iamach...@gmail.com> wrote: >> >> >> > Given a function that returns a random number between 15, write one >> >> > that returns a random number between 17 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 + (T7)*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.
>If RN_7 = T/7, the probability >of a correct guess is < .11 if you always >guess that T = 21 or 22
If the original RNG is uniformly distributed on the interval (1,5), then it's a continuous distribution, so the probability that T = 21 or T = 22 is 0.
And once again, since T/7 only has range 1 to 5, thus it's obviously not uniform on (1,7). It's not even uniform on (1,5), since it has more concentration near the mean (3) than near the ends.
quasi

