
Re: Random numbers
Posted:
Dec 23, 2007 10:46 PM


On Dec 22, 5:25 pm, quasi <qu...@null.set> wrote: > On Sat, 22 Dec 2007 16:30:20 0800 (PST), bill <b92...@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.
Just in case my notation is incorrect; if T = 21, then T mod 7+1 = 1; If T = 35, T mod 7 +1 = 1. The following is the typical result of my simulation.
1 1209 2 1115 3 1180 4 1189 5 1191 6 1131 7 1171 TOT 8186
> > >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.
I was assuming that the original RNG was discrete. > > 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. > I agree!
Bill J > quasi

