Re: RE: Quick "Random[]" question
- To: mathgroup at smc.vnet.net
- Subject: [mg41878] Re: [mg41847] RE: [mg41831] Quick "Random[]" question
- From: Bobby Treat <drmajorbob-MathGroup3528 at mailblocks.com>
- Date: Sat, 7 Jun 2003 11:45:02 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I did a similar experiment, and found it would take about
1.649328667383962*^14
random draws to get a result within 10^-16 of either end-point
f[n_Integer] := Block[{min = 10.^(-n), count = 0, max},
max = 1 - min;
{Timing[While[min < Random[] < max, count++]][[1, 1]], count}]
counts = f /@ Range[4, 8]
{{0.032, 4476}, {0.25, 37250}, {
1.046, 160748}, {8.125, 1236061}, {136.344, 20678316}}
Fit[Log@times[[All, 2]], {1, z}, z]
Exp[%] /. z -> 16 - 3
6.24483 + 2.03783 z
1.649328667383962*^14
I used Regress to check how significant the fit was, and it was VERY
good. On my machine it would take about 29 years:
Fit[Log@save[[All, 1]], {1, z}, z]
Exp[%]Second /. z -> 16 - 3
% /. Second -> Year/(365.25*24*60*60)
-5.61334 + 2.01956 z
9.210255557287763*^8*Second
29.1855 Year
On the other hand, it could happen today, on the next random draw!!
Bobby
-----Original Message-----
From: Wolf, Hartmut <Hartmut.Wolf at t-systems.com>
To: mathgroup at smc.vnet.net
Subject: [mg41878] [mg41847] RE: [mg41831] Quick "Random[]" question
>-----Original Message-----
>From: Jonathan Greenberg [mailto:greenberg at ucdavis.edu]
To: mathgroup at smc.vnet.net
>Sent: Friday, June 06, 2003 3:51 PM
>To: mathgroup at smc.vnet.net
>Subject: [mg41878] [mg41847] [mg41831] Quick "Random[]" question
>
>
>Is it possible to get 0.0 and 1.0 from Random[] (e.g. is the x=Random[]
>0<=x<=1 or 0<x<1 ?)
>
>--j
>
Jonathan,
mathematically speaking, the question appears, to me, to be of no
relevance
(target set of measure zero).
The computational side might be different, but observe:
In[3]:= n = 6;
In[4]:=
(res = {};
With[{min = 10.^(-n + 1), max = 1. - 10^(-n + 1)},
Do[If[(x = Random[]) < min || x > max, res = {res, x}], {10^n}]] ;
Sort[Flatten[res]]) // Timing
In[5]:= % // InputForm
Out[5]//InputForm=
{35.792*Second, {8.169411304711355*^-7,
2.715084457434458*^-6, 3.384771903159169*^-6,
3.453568531851855*^-6, 4.178183919986743*^-6,
5.300288977082681*^-6, 6.6703436910034615*^-6,
8.29779495011354*^-6, 9.257352686970702*^-6,
0.9999932347987964, 0.9999939369474545,
0.9999948585417587, 0.9999961986226781,
0.9999962344951426, 0.9999968296839472,
0.9999982857366351, 0.9999987538196398,
0.9999990610373628, 0.9999993741303179}}
In[6]:= %%[[1]] * 10^10 /. Second -> Year /(365.25*24*60*60)
Out[6]= 11341.8 Year
I simply havn't got that time.
In Help there is a remark:
Random[Real, range, n] generates an ndigit pseudorandom real number.
Both
leading and trailing digits may be chosen as 0.
But, as ever, regard:
In[15]:= Random[Real, {0, 1}, 17]
Out[15]= 0.025225070291350781
In[16]:= Random[Real, {0, 1}, 16]
Out[16]= 0.951953
In[17]:= MachineNumberQ /@ {%%, %}
Out[17]= {False, True}
You may however control the case if you generate random Integers -- of a
certain range -- and convert to reals by yourself.
--
Hartmut Wolf