I looked in my logs. Sadly I have many conversations bitching about variance, but I still found it in like 5 minutes.
Code:
[Thu Feb 14 08:48:30 2013] Ghwerig says, 'I think central limit theorem just says that for any large sample size of independent events/variables that it tends to go like a normal distribution about the mean'
[Thu Feb 14 08:49:11 2013] You say, 'this is correct but'
[Thu Feb 14 08:49:19 2013] You say, 'i thought it also said somethinga bout the rate of convergence'
[Thu Feb 14 08:49:59 2013] Ghwerig says, 'i am not sure abou that'
[Thu Feb 14 08:50:05 2013] Jeremy says, 'so what are the actual odds of 3 robes in a row!'
[Thu Feb 14 08:50:23 2013] You say, 'I think the robe is like 1/3 maybe'
[Thu Feb 14 08:50:26 2013] Jeremy says, 'I've probably seen 5 robes for 40 tunics'
[Thu Feb 14 08:50:32 2013] Jeremy says, 'feels like less to me'
[Thu Feb 14 08:50:32 2013] Ghwerig says, 'but the variance is always proportional to the mean squared, by definition in statistics'
[Thu Feb 14 08:50:34 2013] You say, 'nah its more than than that'
[Thu Feb 14 08:50:50 2013] Jeremy says, 'I just been lucky'
[Thu Feb 14 08:50:56 2013] Jeremy says, 'I'd say it's 1 in 5 or 6'
[Thu Feb 14 08:50:57 2013] You say, 'actually '
[Thu Feb 14 08:51:00 2013] You say, 'let me check'
[Thu Feb 14 08:51:38 2013] Ghwerig says, 'it is tough to do the central limit theorem with a coin flip, because the distribution is bimodal'
[Thu Feb 14 08:51:51 2013] Ghwerig says, 'a spike at tails and a spike at heads'
[Thu Feb 14 08:52:24 2013] Jeremy says, '*binomial'
[Thu Feb 14 08:52:27 2013] You say, 'yes but it rapidly becomes a normal distribution'
[Thu Feb 14 08:52:47 2013] Jeremy says, 'can you really organize heads and tails like that?'
[Thu Feb 14 08:52:47 2013] You say, 'here is my point'
[Thu Feb 14 08:52:56 2013] Ghwerig says, 'but for any randomly distributed variable, CLT says it should be ~gaussian/normally distributed about the mean, and then the expected fluctuations should always go as sqrt N'
[Thu Feb 14 08:53:12 2013] You say, 'well I ran a test and thats def what happened'
[Thu Feb 14 08:53:12 2013] Ghwerig says, 'ok go on'
[Thu Feb 14 08:54:31 2013] Ghwerig says, 'so i remember proving it in high school and in college physics... here is what i remember'
[Thu Feb 14 08:54:49 2013] Sericx says, 'wow i just fell asleep on my keyboard'
[Thu Feb 14 08:55:55 2013] Ghwerig says, 'variance is basically proportional to stddev^2 right?'
[Thu Feb 14 08:56:29 2013] Ghwerig says, 'what is sstdv?'
[Thu Feb 14 08:56:36 2013] Tecmos tells you, 'aww, lol. i was thinking "boy, thatd be funny it it were fischsemmel"'
[Thu Feb 14 08:56:46 2013] You say, 'sorry variance = standard deviation squared by definition'
[Thu Feb 14 08:56:49 2013] You say, 'at least i thought so'
[Thu Feb 14 08:56:54 2013] Ghwerig says, 'yeah'
[Thu Feb 14 08:57:20 2013] Ghwerig says, 'well if you have n events... variance = n stdeve^2'
[Thu Feb 14 08:57:49 2013] You say, 'ahh ok i see where you are going with this'
[Thu Feb 14 08:57:52 2013] Jeremy says, 'can you really quantify variance between discrete drops like that?'
[Thu Feb 14 08:58:01 2013] Jeremy says, 'i suck at stats'
[Thu Feb 14 08:58:06 2013] Jeremy says, 'but doesn't seem right'
[Thu Feb 14 08:58:16 2013] Ghwerig says, 'if you knew the actual percentages of drops... you could easily do it'
[Thu Feb 14 08:58:37 2013] Jeremy says, 'maybe I just can't wrap my brain around what it actually describes'
Ghwerig and I were basically saying the same thing about CLT (that the standard deviation of an average goes down with sample size as sqrt(n)), which Wikipedia says better:
Quote:
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By the law of large numbers, the sample averages converge in probability and almost surely to the expected value µ as n → ∞. The classical central limit theorem describes the size and the distributional form of the stochastic fluctuations around the deterministic number µ during this convergence. More precisely, it states that as n gets larger, the distribution of the difference between the sample average Sn and its limit µ, when multiplied by the factor √n (that is √n(Sn − µ)), approximates the normal distribution with mean 0 and variance σ2. For large enough n, the distribution of Sn is close to the normal distribution with mean µ and variance σ2/n
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Note that he mentions how the variance could easily be computed 'if only we know the drop probabilities'.
I really don't see why you find this confusing. The random variable in question is the number of tunics, robes, and staves after killing N kings. The average is the expected number of each, and the variance represents how large the deviation from the average is likely to be.