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


Re: Random numbers
Posted:
Dec 22, 2007 2:04 PM


On Sat, 22 Dec 2007 14:00:57 0500, quasi <quasi@null.set> wrote:
>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?
I meant: It should be (exactly) 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

