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Topic review (newest first)
Start with the first two numbers and end with the last two, listing each combination.
Hmm, and the rows are obtained how?
and for any n
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.
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Explain in simple words please
That does suggest without replacement. The answer is (59 + 1 ) / 3 = 20.
"The teacher picks out two tickets"
If there picking without replacement then the answer is 20. If not the answer in post #2 holds.
I am getting 20 as well.
There is no replacement?
I am getting 20
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|?