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Topic review (newest first)

Agnishom
2013-04-16 00:07:50

gOt it
Thanks smile

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

Explain in simple words please hmm

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.


When you have time please sign up over here:

https://brilliant.org/

Agnishom
2013-04-13 23:52:17

Explain in simple words please hmm

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|?

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