If we have a box that contains 1000000 balls numbered from 1 to 1000000.

if we take "K" balls without replacement. let X be the maximum number and y be the minimum number in the K balls.

What is the expected value E(x-y) as function of "K".

Printable View

- Apr 30th 2012, 01:44 PMbillobilloExpected value of balls in box (a challenging one)
If we have a box that contains 1000000 balls numbered from 1 to 1000000.

if we take "K" balls without replacement. let X be the maximum number and y be the minimum number in the K balls.

What is the expected value E(x-y) as function of "K". - Apr 30th 2012, 02:27 PMPlatoRe: Expected value of balls in box (a challenging one)
@billobillo

You will never understand this question unless you yourself sit and work with the numbers.

May I suggest that you cut the question down to 100 balls an let K=8.

List the smallest eight numbers. What is

List the larest eight numbers. What is

List any eight numbers. What is

Now what is the maximum for ?

Now what is the minimum for ?

Now what is ?

The think about number partitions?

When you have done that. Tell us what you find. - Apr 30th 2012, 02:48 PMMooRe: Expected value of balls in box (a challenging one)
- Apr 30th 2012, 02:59 PMhttrRe: Expected value of balls in box (a challenging one)
The title is a bit misleading...

Try it Moo, but maybe not start with K=8...

if K=2, you draw 2 balls out of 100, what is the expected value of the bigger numbered ball?

Now you draw 3 balls...

Then you should get it by now.

prove by using principle of symmetry - Apr 30th 2012, 03:29 PMPlatoRe: Expected value of balls in box (a challenging one)
- Apr 30th 2012, 11:39 PMbillobilloRe: Expected value of balls in box (a challenging one)
Thanks for your replies, before posting this topic, I worked on a sample of 7 balls with K=3 and I was able to find E(x) and E(y) as function of K but not E(x-y),

I'm not a math specialist but I guess that x and y are not independent events, any suggestions? - May 1st 2012, 12:12 AMhttrRe: Expected value of balls in box (a challenging one)
E(x-y) is always E(x)-E(y), you are confusing with E(XY) which required independence to factorize