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.

I'll take a SWAG and say 100...

98 ?????


cheers
SC

would it be 100-n-2?

well, for n=2, by 'common sense' you might guess the answer to be around 50.

i tried to use a hand-waving 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.

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

100*n/(n+1) is what pops into my mind

100 * (n-1) / (n+1) has my money.
and Excel seems to agree.

oops. edited again... typing while working spreadhseet :-)

So, discrete integers and not continuous numbers?

Nice ninja edit

guilty.

ahhhh... is the answer E=mc2..?

Sorry I made a mistake. The answer is in fact 'yo mamma!'

Silly me

continuous, but giving examples it is easier to stick to integers

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 (n-1) interval between the smallest and the largest, therefore the length is (n-1)*100/(n+1)

thats wot i sed

But it's really what I said...in less words...and without an explanation

sorry you wuz beein succinct

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.

(c) Blue........