Why maths textbooks when you can have Wikipedia?

[Phy6explorer]

Why?

Nothing is going to prevent you from doing it, but why do it?
I,mean, I know you won't do it, will you?Why will someone want to pollute a good source of information?

 

[kenewbie]

Nothing is going to prevent you from doing it, but why do it?
I,mean, I know you won't do it, will you?Why will someone want to pollute a good source of information?

For the same reason people kick lampposts' until the streetlight goes out I guess. Because they can.

k

 

[leon1127]

Quoted from Wiki

Proof of the central limit theorem

For a theorem of such fundamental importance to statistics and applied probability, the central limit theorem has a remarkably simple proof using characteristic functions. It is similar to the proof of a (weak) law of large numbers. For any random variable, Y, with zero mean and unit variance (var(Y) = 1), the characteristic function of Y is, by Taylor's theorem,

\varphi_Y(t) = 1 - {t^2 \over 2} + o(t^2), \quad t \rightarrow 0

where o (t2 ) is "little o notation" for some function of t that goes to zero more rapidly than t2. Letting Yi be (Xi − μ)/σ, the standardized value of Xi, [it is easy to see] that the standardized mean of the observations X1, X2, ..., Xn is

Z_n = \frac{n\overline{X}_n-n\mu}{\sigma\sqrt{n}} = \sum_{i=1}^n {Y_i \over \sqrt{n}}.

By [simple properties] of characteristic functions, the characteristic function of Zn is
[itex]
\left[\varphi_Y\left({t \over \sqrt{n}}\right)\right]^n = \left[ 1 - {t^2 \over 2n} + o\left({t^2 \over n}\right) \right]^n \, \rightarrow \, e^{-t^2/2}, \quad n \rightarrow \infty.
[\latex]
But, this limit is just the characteristic function of a standard normal distribution, N(0,1), and the central limit theorem follows from the Lévy continuity theorem, which confirms that the convergence of characteristic functions implies convergence in distribution.
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http://en.wikipedia.org/wiki/Central_limit_theorem

Look at the squared bracket, and see if they are trivial

 

[jtbell]

Why will someone want to pollute a good source of information?

Because he sincerely believes that he is right and most everybody else is wrong.

 

[kuahji]

I'll have to admit, wikipedia has come a long way since it first came out with mathematics. With things like statistics, you do have to be careful with the different notation for variables. I still however would take a decent textbook any day over wikipedia because a textbook will "teach" you the material while wikipedia usually just lists it quick. Also textbooks have practice problems, while wikipedia does not.