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#26 2006-12-28 07:54:44
- krassi_holmz
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- Registered: 2005-12-02
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Re: expected number??
Sorry for the ten posts.
Now - a little break
IPBLE: Increasing Performance By Lowering Expectations.
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#27 2006-12-28 17:06:26
- George,Y
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- Registered: 2006-03-12
- Posts: 1,379
Re: expected number??
Have you used my model?
Acctually it has a little error-it sumes the amount of bins is no lesser than that of balls. Once the former exceeds the latter, the probability of the bins amount of seperate balls needs remodelling-after all you can only throw a ball in a repeated bin among all bins each already with one ball in it.
X'(y-Xβ)=0
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#28 2006-12-29 00:27:05
- krassi_holmz
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- Registered: 2005-12-02
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Re: expected number??
No I haven't.
this doesn't depend of n. Using Pingenhole proncipe, my sum ends with b+1 balls, because it's thoughtless to go further.
I used something like this - I'm cuonting all the possible combinatins with k balls and computing the probability to make a combination of k balls, multyplying them, and summazing for all k form 2 balls to b+1 balls. This gives me the aritmetic mean of the wheighted elements in the list, so the expected number of balls. It's tricky to understand, that the probability to get a combination with mare balls is less than the probability to get a combination with less balls.
And, as you can see from the picture above, the formula works!
Last edited by krassi_holmz (2006-12-29 00:29:43)
IPBLE: Increasing Performance By Lowering Expectations.
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#29 2006-12-29 15:55:12
- George,Y
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- Registered: 2006-03-12
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Re: expected number??
The combination is okay, but the S,L,E functions are obtruse.
X'(y-Xβ)=0
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#30 2006-12-30 03:46:03
- krassi_holmz
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- Registered: 2005-12-02
- Posts: 1,905
Re: expected number??
The L function is the result.
In the above plot the ponts represent the information given by Ricky in his post. So the L functtion is the answer.
The S function was defined by me to help myself. It gives "the number of leafs of depth k in the characteristic tree of the problem".
I'm not sure you'll undersand this, because i can't explain it. I've made to pictures for me, but I'll post them.
The E function is a mathematical function:
http://mathworld.wolfram.com/En-Function.html
Last edited by krassi_holmz (2006-12-30 03:47:12)
IPBLE: Increasing Performance By Lowering Expectations.
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