Merry Christmas and a Happy New Year P99

[Waedawen]

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

[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.

[Jay F Kay]

I find it hard to believe someone would spend time on christmas crunching numbers on fungi drops, but there it is. You're sick, and you need help.

[Breaken]

So you are considering the king to be the variable. I took the drops to be the variable. The drops are not iid, and if you are calculating the probability of the drops, you should consider the drops as the variable. Either way though, the CLT specifically mentions, a 'large' random sample (large number of kings) of random variables (drops).

[quido]

Red and Yellow make Orange.

Bet you guys didn't know that.

[Lojik]

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

Red and Yellow make Orange.

Bet you guys didn't know that.

Red and Blue makes Neckbeards

[quido]

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[Troubled]

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

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Did Borgias end for good btw?

[Raev]

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

So you are considering the king to be the variable. I took the drops to be the variable. The drops are not iid, and if you are calculating the probability of the drops, you should consider the drops as the variable. Either way though, the CLT specifically mentions, a 'large' random sample (large number of kings) of random variables (drops).

I don't quite understand what you mean by the drops vs the king as the choice of the random variable. The multinomial distribution seems very natural to me as it mimics how the loot table works. Are you suggesting that it is better to model it with three separate boolean variables, i.e. P(Tunic), P(Robe), and P(Staff)? Even here, I don't see why each variable would not be IID wrt other instances of itself, and I would think CLT would apply just fine. In other words, the average number of tunics per king should approach the mean and have a gaussian distribution even though the event itself is a discrete 0/1.

P.S. Jeremy, where's my 1M pp