  
14.11.2011, 15:16
  Forum Legend   Join Date: Oct 2009 Location: Basel
Posts: 14,952
Groaned at 295 Times in 199 Posts
Thanked 19,020 Times in 8,000 Posts
  A question for the math geeks
Take the interval of real numbers [0,100].
From this interval, n different numbers are picked randomly, where n>1.
What is the expected difference between the largest and smallest number picked for a given value of n? (assume uniform distribution, where required)
Happy to hear an answer for the case n=2, as well as the more general case for arbitrary integer values of n>1.
Last edited by Phil_MCR; 14.11.2011 at 15:38.

14.11.2011, 15:17
  Forum Veteran   Join Date: Aug 2011 Location: ZURICH
Posts: 2,335
Groaned at 173 Times in 124 Posts
Thanked 3,384 Times in 1,536 Posts
  Re: A question for the math geeks
I'll take a SWAG and say 100...

14.11.2011, 15:25
  Forum Veteran   Join Date: Jan 2008 Location: Zug
Posts: 2,139
Groaned at 40 Times in 27 Posts
Thanked 3,047 Times in 1,239 Posts
  Re: A question for the math geeks
98 ?????
cheers
SC

14.11.2011, 15:32
  Forum Veteran   Join Date: Feb 2011 Location: geneva
Posts: 1,476
Groaned at 29 Times in 16 Posts
Thanked 1,508 Times in 695 Posts
  Re: A question for the math geeks
would it be 100n2?

14.11.2011, 15:50
  Forum Legend   Join Date: Oct 2009 Location: Basel
Posts: 14,952
Groaned at 295 Times in 199 Posts
Thanked 19,020 Times in 8,000 Posts
  Re: A question for the math geeks
well, for n=2, by 'common sense' you might guess the answer to be around 50.
i tried to use a handwaving geometric argument and get an answer 37.5. which seems to be a reasonable answer and goes with my 'gut feeling'.
if it is right, i would be happy to see a rigorous proof and also to extend a result for n>2.
i'm sure the IT geeks can come up with an empirical answer by statistical trials.

14.11.2011, 15:53
  Forum Legend   Join Date: Oct 2009 Location: Basel
Posts: 14,952
Groaned at 295 Times in 199 Posts
Thanked 19,020 Times in 8,000 Posts
  Re: A question for the math geeks
example for n=2. pick the first number at random, it is 35. pick the 2nd number at random it is 67. difference between the two is: 32.
to get an answer of 98, you'd have to pick: 0, 98; 1, 99, or 2, 100 (just taking whole number examples). so 98 doesn't seem like a likely answer 
14.11.2011, 15:54
  Re: A question for the math geeks
100*n/(n+1) is what pops into my mind

14.11.2011, 15:55
  Forum Veteran   Join Date: Feb 2006 Location: Zurich
Posts: 1,631
Groaned at 31 Times in 24 Posts
Thanked 1,279 Times in 628 Posts
  Re: A question for the math geeks
100 * (n1) / (n+1) has my money.
and Excel seems to agree.
oops. edited again... typing while working spreadhseet :)

14.11.2011, 15:56
  Forum Veteran   Join Date: Aug 2011 Location: ZURICH
Posts: 2,335
Groaned at 173 Times in 124 Posts
Thanked 3,384 Times in 1,536 Posts
  Re: A question for the math geeks
So, discrete integers and not continuous numbers?

14.11.2011, 15:58
  Re: A question for the math geeks  Quote:      100 *n / (n+1) has my money.
and Excel seems to agree.      Nice ninja edit 
14.11.2011, 16:00
  Forum Veteran   Join Date: Feb 2006 Location: Zurich
Posts: 1,631
Groaned at 31 Times in 24 Posts
Thanked 1,279 Times in 628 Posts
  Re: A question for the math geeks  Quote:      Nice ninja edit      guilty. 
14.11.2011, 16:03
  Re: A question for the math geeks
ahhhh... is the answer E=mc2..? 
14.11.2011, 16:06
  Re: A question for the math geeks
Sorry I made a mistake. The answer is in fact 'yo mamma!'
Silly me 
14.11.2011, 16:10
  Forum Legend   Join Date: Oct 2009 Location: Basel
Posts: 14,952
Groaned at 295 Times in 199 Posts
Thanked 19,020 Times in 8,000 Posts
  Re: A question for the math geeks  Quote:      So, discrete integers and not continuous numbers?      continuous, but giving examples it is easier to stick to integers 
14.11.2011, 16:10
  Forum Legend   Join Date: Feb 2010 Location: CH
Posts: 3,200
Groaned at 86 Times in 70 Posts
Thanked 5,788 Times in 2,254 Posts
  Re: A question for the math geeks
Since you assume an uniform distribution, n points will split the range [1..100] in (n+1) smaller intervals. Each interval length is 100/(n+1).
The n points have (n1) interval between the smallest and the largest, therefore the length is (n1)*100/(n+1)

14.11.2011, 16:12
  Forum Veteran   Join Date: Feb 2011 Location: geneva
Posts: 1,476
Groaned at 29 Times in 16 Posts
Thanked 1,508 Times in 695 Posts
  Re: A question for the math geeks  Quote:      Since you assume an uniform distribution, n points will split the range [1..100] in (n+1) smaller intervals. Each interval length is 100/(n+1).
The n points have (n1) interval between the smallest and the largest, therefore the length is (n1)*100/(n+1)      thats wot i sed

14.11.2011, 16:13
  Re: A question for the math geeks  Quote:      thats wot i sed      But it's really what I said...in less words...and without an explanation 
14.11.2011, 16:18
  Forum Veteran   Join Date: Feb 2011 Location: geneva
Posts: 1,476
Groaned at 29 Times in 16 Posts
Thanked 1,508 Times in 695 Posts
  Re: A question for the math geeks  Quote:      But it's really what I said...in less words...and without an explanation      sorry you wuz beein succinct

14.11.2011, 16:32
  Member   Join Date: Jun 2010 Location: Geneva
Posts: 180
Groaned at 1 Time in 1 Post
Thanked 209 Times in 93 Posts
  Re: A question for the math geeks
MrVertigo gave the simplest complete explanation, and should win the cookie for doing someone else's homework for them.
Other answers were also right, or at least converged on right fairly rapidly
BTW, the actual interval is irrelevant, since it only scales the answer.
For extra points, take into account that the expected difference between two integers should probably be an integer...the answers given so far are generally not integers.

14.11.2011, 16:34
  Forum Legend   Join Date: May 2010 Location: In the kitchen at parties.
Posts: 4,540
Groaned at 204 Times in 120 Posts
Thanked 6,078 Times in 2,378 Posts
  Re: A question for the math geeks
(c) Blue........

Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)   Thread Tools   Display Modes  Linear Mode 
Posting Rules
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts HTML code is Off    All times are GMT +2. The time now is 02:19.  