mersenneforum.org Cant seem to figure this out
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 2006-03-15, 03:40 #1 Carlsagan43   Mar 2006 1012 Posts Cant seem to figure this out Suppose I have x number of blocks numbered 1-x. There are now 2^x possible combinations of blocks. I sum the amount on the blocks that I have picked frm the group of blocks to get a range of 0 - ((x^2)+x)/2. What is the distribution of sums accoring to this pattern? Example: here are the blocks I have with a distribution table beneath it: 1 2 3 4 5 6 7 ------------ 1 0 1 1 1 0 1 So, I have 1*1+ 2*0+ 3*1+ 4*1+ 5*1+ 6*0+ 7*1= 20 How many 20s, or any sum for that matter from any certain number of blocks?
2006-03-15, 12:28   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by Carlsagan43 Suppose I have x number of blocks numbered 1-x. There are now 2^x possible combinations of blocks. I sum the amount on the blocks that I have picked frm the group of blocks to get a range of 0 - ((x^2)+x)/2. What is the distribution of sums accoring to this pattern? Example: here are the blocks I have with a distribution table beneath it: 1 2 3 4 5 6 7 ------------ 1 0 1 1 1 0 1 So, I have 1*1+ 2*0+ 3*1+ 4*1+ 5*1+ 6*0+ 7*1= 20 How many 20s, or any sum for that matter from any certain number of blocks?
Your question is not well posed. It lacks too much information

You have labelled some blocks 1 to x.

(1) Does the VALUE of each block (not just its label) equal its index?
(2) You do not state how many blocks are being summed.

However, for moderately large set being summed, the answer to your
question is given by the Central Limit Theorem. (look it up).
The distribution for your sum will be approximately normal.

The distribution for the sum of two uniform random variables looks like a tent:

/ \
/ \
/ \

For 3 r.v's it looks like:

/\
/ \
/ \
. .
. .
. .

i.e. there is a 'break' in the sides of the tent where the slope changes.

As the number of items in the sum increases, the distribution becomes
more normal.

 2006-03-15, 19:29 #3 Mystwalker     Jul 2004 Potsdam, Germany 3×277 Posts The example seems like it can answer those questions: (1) Yes (with this in mind, the "0 - ((x^2)+x)/2" makes sense as well). (2) Every combination of 0s and 1s can be assigned to the blocks. Those blocks that have a 1 get summed up (alternatively, you can simply do a linear combination). Unfortunately, I'm unable to give an answer to this. But I'm not sure whether Mr. "No abortion!" comes back after all...
 2006-03-15, 21:37 #4 Carlsagan43   Mar 2006 5 Posts To simplify: 1*a + 2*b + 3*c + 4*d + 5*e + 6*f + 7*g = x Where the variables a, b, c, d, e, f, and g hold values of either 1 or 0 for each variable. What is the what is the range of x? (distibution)

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