模倣子 Discrete Normal Distributions

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Introduction

I'm still trying to take it all in, but a buddy of mine clued me in to the idea of Pascal's Triangle producing a distribution, a normal one, and a discrete one, in fact, for an experiment consisting of a series of binomial trials.

His idea is that this discrete distribution may be used to assess the reliability of a poll, for example, taken as a sample from a population about preference for Candidate A versus Candidate B, for instance. I may be misquoting, and I'm still chewing on this idea. He said that this information may be gotten from the "two tails" of the discrete distribution, outside of the probability value of the given sample.

Pascal's Triangle

					0	1	0
				0	1		1	0
			0	1		2		1	0
		0	1		3		3		1	0
	0	1		4		6		4		1	0
0	1		5		10		10		5		1	0

An Example

First off, the fifth row of Pascal's Triangle, as above, is "1, 4, 6, 4, 1" which totals to 16. What does this mean? An experiment of 16 trials, 16 coin flips, will be distributed over no heads and 16 tails to 16 heads and no tails.

It might be simpler to start with the "1, 2, 1" row, the third row. There are four trials, 16 possible permutated outcomes, or 5 combinatorial outcomes.

{ tail, tail, tail, tail}

{ head, tail, tail, tail }

{ head, head, tail, tail }

{ head, head, head, tail }

{ head, head, head, head }

TTTT	TTTH	TTHH	TTHT
THTT	THTH	THHH	THHT
HTTT	HTTH	HTHH	HTHT
HHTT	HHTH	HHHH	HHHT

So the probability of getting one heads flip only is only one in sixteen. The chance of two of each is 50%. 

More Will Be Revealed

I need to get back in touch with my buddy about how to interpret the tails of this distribution, and then how to use it all to assess the likelihood of given results.