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".
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".
@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.
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
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?