quasi
Posts:
12,057
Registered:
7/15/05


Re: Random numbers
Posted:
Dec 22, 2007 2:00 PM


On Sat, 22 Dec 2007 13:51:57 0500, quasi <quasi@null.set> wrote:
>On Sat, 22 Dec 2007 10:43:27 0800 (PST), vr <simple.popeye@gmail.com> >wrote: > >>On Dec 22, 11:35 pm, quasi <qu...@null.set> wrote: >>> On Sat, 22 Dec 2007 10:32:37 0800 (PST), vr <simple.pop...@gmail.com> >>> wrote: >>> >>> >>> >>> >>> >>> >On Dec 22, 11:16 pm, 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 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. > >Yes, but not uniformly. > >What's the chance of getting exactly 35? > >If it was a uniform distribution it would be 1/29, right?
Of course, that's assuming S is a uniformly distributed integer variable on {1,2,3,4,5}.
If instead, S is a uniformly distributed continuous variable on (1,5) then we can ask  what's that chance of getting a result more than 34? It should be at least 1/28, right? But it's easily seen to be a lot less than that (the probability is bounded above by 1/2^(14)).
quasi

