This is an odd distribution... I think it may somehow be related to the
binomial distribution, but I'm not certain.
The idea is difficult to explain, so here's a "real-life" example of
generating the distribution:
I have four coins in my hand. Each coin has a number on both sides. All
coins have a zero on one side, and the other side has a number from 1 to 4.
I then hurl the handful of coins at the ground, then add up the values of
all the coins.
Here's a list of every possible combination of ways the coins may land, with
the corresponding total.
Coins Total
0 0 0 0 0
1 0 0 0 1
0 2 0 0 2
1 2 0 0 3
0 0 3 0 3
1 0 3 0 4
0 2 3 0 5
1 2 3 0 6
0 0 0 4 4
1 0 0 4 5
0 2 0 4 6
1 2 0 4 7
0 0 3 4 7
1 0 3 4 8
0 2 3 4 9
1 2 3 4 10
If you plot the histogram, you can see the faint shadow of a bell curve
there.
Histograms of totals:
Total Quantity
0 1
1 1
2 1
3 2
4 2
5 2
6 2
7 2
8 1
9 1
10 1
Well then, with all that being said, my question: what kind of distribution
is this anyway? I know I can calculate everything by hand for a small number
of coins, but say I had 100 coins, then I would need an equation to generate
the distribution.
Any help would be greatly appreciated...
Derek Ross.
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