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Agnishom
2013-04-16 00:07:50

gOt it
Thanks

gAr
2013-04-15 23:53:04

Start with the first two numbers and end with the last two, listing each combination.

(2-1), (3-1), ... (59-1)
(3-2), (4-2) ... (59-2)
.
.
(58-57), (59-57)
(59-58)

Agnishom
2013-04-15 23:46:16

Hmm, and the rows are obtained how?

gAr
2013-04-15 23:31:27

Hi,

Let's begin with the list of |i - j| possibilities :
1, 2, 3, 4, ... , 58
1, 2, 3, 4 ..  57
1, 2, 3, .. 56
.
.
.
1, 2
1

Each number from every row is equiprobable
Hence, the expectation:

and for any n

bobbym
2013-04-13 23:56:48

Hi;

This is the answer from my notes.

There are n(n-1) ways to pick two numbers from the unit interval 1 ... n.

If they are ordered high and low then there are:

ways.

The standard way now to do this is to look at the ordered pairs. There is 1 way for 2 to be the maximum and 2 ways for 3 to be the maximum and there are generally m-1 ways for m to be the maximum. Using the formula for expected value or expected number:

For the second part, you do it in the same way. There are
still n (n-1)/2 ways to arrange n numbers with high and low.

Now you go through the numbers in the same way. 1 is the lowest n-1 times. 2 is the lowest n - 2 times. n can never be the lowest. n-1 is the lowest one time so generally m is lowest n - m times. We use the same formula for expected value:

Now for the difference.

Just subtract the expected value of the lowest from the highest.

The absolute value is implied in there.

https://brilliant.org/

Agnishom
2013-04-13 23:52:17

bobbym
2013-04-13 23:50:13

That does suggest without replacement. The answer is (59 + 1 ) / 3 = 20.

anonimnystefy
2013-04-13 23:46:10

"The teacher picks out two tickets"

bobbym
2013-04-13 23:43:49

If there picking without replacement then the answer is 20. If not the answer in post #2 holds.

anonimnystefy
2013-04-13 23:40:55

I am getting 20 as well.

bobbym
2013-04-13 23:31:22

There is no replacement?

Agnishom
2013-04-13 23:28:26

I am getting 20

bobbym
2013-04-13 23:23:45

Hi;

Agnishom
2013-04-13 23:00:46

A school is running a raffle for two prizes. 59 tickets were sold for the raffle, numbered 1,…,59. All the tickets are put into a hat and a teacher picks out two tickets which have numbers i and j from the hat. What is the expected value of |i−j|?