Merry Christmas and a Happy New Year P99

[quido]

the variance of the values themselves, ya moran, not their respective probabilities

Imagine a collection of heights - their variance isn't the variance of their respective probabilities.

ya moran

just admit you were trying to sound smart in /say and that what you said was actually complete nonsense - I'll find the screenshot when I get home in a day or two

[quido]

I admit I am awful at statistics, but I do know enough to realize that what you had said was total nonsense! You cannot find the variance of a set of non-numeric values. Sure you can find the variance of the set of their respective probabilities, but this is something else entirely.

[Raev]

I looked in my logs. Sadly I have many conversations bitching about variance, but I still found it in like 5 minutes.

[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:

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

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.

[Waedawen]

Dude you guys are fucking losers lol

[quido]

NERDS

[Waedawen]

That whole back and forth between Loraen and the Variance and the Formulas and the Numberquest

Jesus Christ man maybe you should just quit EQ and not come grovelling back this time

[Waedawen]

Raev, excuse me. Hard to keep track and all.

[Jfertal]

Originally Posted by quido [You must be logged in to view images. Log in or Register.]

no video like this will ever hold a candle to Eccezan's

the original was the best.

[Breaken]

[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'

The Central Limit Theorem states:

The sample mean of a large random sample of random variables with mean μ and finite variance σ² has approximately a normal distribution with mean μ and variance σ²/n.

It does not address convergence because not all instances have the same rate of convergence. The fact is that the drop rates are not identical, so this situation is not iid. To get a 'standard normal distribution', you need to use another variable, (X - μ)/σ.

[Raev]

I don't see why you think the situation is not IID. Each instance of the spore king is independent and identical. As you kill more and more, the expected number of drops should be N(U*n, S^2) where u = [0.65, 0.30, 0.05] and S^2 would be the diagonal entries of the matrix I calculated earlier.