cdfsrule wrote:
>
> Yes, here we go again and again...
>
> Harry Porterwrote:
> > Variance, as a mathematical measure, best describes the range of
> > outcomes for an event that has a true "normal" distribution (e.g.
> > the flipping of a penny or roll of a die).
>
> Neither the flipping of a penny nor the roll of a die produces a
> "normal" distribution of outcomes (normal meaning gaussian or
> bell-curve). Not even close. Both should produce even distributions
> (discrete even distributions).
>
> If you summed the output of multiple rolls, or multiple die, as the
> number things you summed increases, the distribution would begin to
> look more "normal". In that case, the standard deviation would go as
> 1/sqrt(N) where N is the number of rolls you summed up, since there
> is NO correlation between die.
Yes, perhaps, here we go again (and again) ...
Unless I'm mistaken, it would seem that my wording wasn't precise
enough for you (or, to be more specific, that in an atypical manner I
spared a few too many words and made erred by presuming that what was
missing would be inferred).
You're absolutely correct, if you chart the distribution of heads vs.
tails in multiple flips of a coin, you'd expect an even distribution
... that is, the number of each should be roughly even. This can also
be referred to as a discrete uniform distribution (I had to look that
one up).
What I had in mind was the distribution of the cumulative number of
observed heads (or tails) as the number of flips increases. But once
again, I'm imprecise in describing this as a normal distribution ...
for the term "normal distribution" describes a continuous probability
distribution -- were the distribution of head tosses truly a normal
distribution (rather than a discrete distribution), then there would
be a probability assigned for an event such as 5.363 heads being observed.
To be more accurate, I should have said that the two examples were
discrete distributions that approximate a normal distribution (to
again make the distinction in my post that vp results, instead, do not).
Now, certainly this more accurately presents the information (although
I have no doubt that if you're inclined to do so, you can still point
to some inaccuracies). My suspicion, however, is that most here would
prefer that you not encourage me in going on at such length when it
doesn't really add much clarity to my original point (as far as the
vpFREE rank and file go).
- H.
