An expectation problem:

bobbym · 2012-07-29 08:16:11

Yes, it is quite small.

anonimnystefy · 2012-07-29 08:17:39

How small?

bobbym · 2012-07-29 08:20:33

I do not know. But looking at the data the values are very close.

anonimnystefy · 2012-07-29 08:24:25

Oh. Okay.

bobbym · 2012-07-29 08:26:22

To get the sd we would have to run the simulation many times and use the formula. But by inspection you can see the dispersion is going to be small.

phrontister · 2012-07-29 18:56:21

Hi Bobby and stefy,

I've run several 10,000-cycle simulations in LB and each result was a smidge over 223.0. The result of a 100,000 cycle was 223.03524.

My Excel results varied more, but all were still only just < or > 223. I only tested up to about 1,000 cycles, which would account for the variation difference between the two programs.

anonimnystefy · 2012-07-29 19:52:40

Hi phrontister

I started running 10 100000-cycles, but I wasn't at the computer long enough to check.

bobbym · 2012-07-29 23:11:39

Hi phrontister;

I got a shade over 223 also.

phrontister · 2012-07-30 01:44:11

Hi Bobby,

Here's my M code. As you'll see, I was thinking LB while coding M...but it works.

My initial code was slow because I was testing for '200 ones' from the first pick ( ), but changing the test to commence after 199 picks reduced processing time to 1/7th of previous.

My LB code for 100,000 cycles took well over 9 hours c.f. M's 271 seconds.

In[1]:= Timing[sum = 0; c = 0; s = Table[0, {1000}];
         N[While[c < 100000, t = 199; ss = s;
          Do[ss[[RandomInteger[{1, 1000}]]] = 1, {t}] 
           While[Count[ss, 1] < 200, ss[[RandomInteger[{1, 1000}]]] = 1;t++]; 
          sum = sum + t; c++]; sum/c]]

Out[1]= {270.985, 223.00152}

So, again, just a touch > 223.

Last edited by phrontister (2012-08-03 20:23:22)

bobbym · 2012-07-30 03:39:48

Hi phrontister;

That is fine. It is okay to go from one language to another looking for the same type of commands in each language.

phrontister · 2012-07-30 03:48:34

Hi Bobby,

That's really the only way I'll get anywhere with M for now. Anything that would require more dedicated study effort will have to wait until I get more time to be able to spend at it...but little by little I'm picking a few things up. Thanks for dangling the "extra credit" carrot...it motivated me.

bobbym · 2012-07-30 03:55:30

Hi;

Go at your own pace. You did well.

gAr · 2013-09-02 01:04:06

J:

sim =: monad define 
cnt =: 0
a =: y$0
while. (+/a) < 200 do.
  a =: 1 (?y)} a
  cnt =: cnt + 1
end.
return. cnt
)
(+/%#) (sim "0) 1000$1000  NB. (sim&+) also works

≈ 223.024

There may be a way to eliminate the loop and speed up.

bobbym · 2013-09-02 01:11:25

Hi gAr;

What was your time?

gAr · 2013-09-02 01:58:45

Hi bobbym,

About 15.8 seconds for 10000 trials.

(6!:2) '%. (+/%#) (sim "0) 10000$1000'  NB. gets the running time

bobbym · 2013-09-02 02:27:07

Hi;

Okay, thanks.

gAr · 2013-09-02 02:34:51

What's the time taken by the mathematica code?

bobbym · 2013-09-02 02:59:47

Hi;

I do not know, I never ran a simulation of this one that did not use the answer to speed it up.

I am trying phrontister's code.

gAr · 2013-09-02 03:10:47

That's okay, he has mentioned his time for simulation.
I thought you had posted your code in this thread.

bobbym · 2013-09-02 03:16:10

His code will do about 30 seconds but it is procedural and does not make use of the faster functional paradigm. Also it is not compiled.

gAr · 2013-09-02 03:19:27

That's right.

gAr · 2013-12-08 04:41:39

Loopless J code, about 30x faster:

sim =: 3 : '1+{.I.200=+/\~:?1000#1000'
(+/%#)(sim "0) 100000#0

Math Is Fun Forum

#26 2012-07-29 08:16:11

Re: An expectation problem:

#27 2012-07-29 08:17:39

Re: An expectation problem:

#28 2012-07-29 08:20:33

Re: An expectation problem:

#29 2012-07-29 08:24:25

Re: An expectation problem:

#30 2012-07-29 08:26:22

Re: An expectation problem:

#31 2012-07-29 18:56:21

Re: An expectation problem:

#32 2012-07-29 19:52:40

Re: An expectation problem:

#33 2012-07-29 23:11:39

Re: An expectation problem:

#34 2012-07-30 01:44:11

Re: An expectation problem:

#35 2012-07-30 03:39:48

Re: An expectation problem:

#36 2012-07-30 03:48:34

Re: An expectation problem:

#37 2012-07-30 03:55:30

Re: An expectation problem:

#38 2013-09-02 01:04:06

Re: An expectation problem:

#39 2013-09-02 01:11:25

Re: An expectation problem:

#40 2013-09-02 01:58:45

Re: An expectation problem:

#41 2013-09-02 02:27:07

Re: An expectation problem:

#42 2013-09-02 02:34:51

Re: An expectation problem:

#43 2013-09-02 02:59:47

Re: An expectation problem:

#44 2013-09-02 03:10:47

Re: An expectation problem:

#45 2013-09-02 03:16:10

Re: An expectation problem:

#46 2013-09-02 03:19:27

Re: An expectation problem:

#47 2013-12-08 04:41:39

Re: An expectation problem:

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