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Show that $\sqrt{2\pi n}\Pr(S_n=k)\to\exp(-x^2/2)$

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#probability-theory #poisson-distribution #central-limit-theorem
309
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Proof that this distribution is N(0,1)?

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#statistics #central-limit-theorem
42
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Weird behaviour of CLT's application to binomial.

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#statistics #problem-solving #statistical-inference #estimation #central-limit-theorem
44
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Gaussian approximation for general Covariance matrices

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#probability-theory #central-limit-theorem
1.3k
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Example 19.6 in van der Vaart: show that the class of indicator functions is P-Glivenko-Cantelli and P-Donsker

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#probability-theory #proof-verification #stochastic-processes #proof-explanation #central-limit-theorem
514
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If a class of functions $\mathcal{F}$ is a Glivenko-Cantelli class then it is also a Donsker class?

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#probability-theory #statistics #stochastic-processes #central-limit-theorem #law-of-large-numbers
228
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Help for example 19.7 in van der Vaart: show that a parametric class of functions with Lipschitz condition is Donsker

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#probability-theory #stochastic-processes #uniform-convergence #central-limit-theorem #lipschitz-functions
2.1k
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Calculating the expected value and variance of $n$ independent observations of $X$

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#probability #random-variables #central-limit-theorem #variance
1.8k
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Central Limit Theorem for symmetric Beta Distribution

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#probability #central-limit-theorem
1k
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Lindeberg Condition for a sequence of discrete random variables.

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#probability #probability-theory #central-limit-theorem
527
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Central Limit Theorem for Multinomial Trials to prove weak convergence to Brownian Bridge

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#probability #probability-theory #central-limit-theorem
319
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Chernoff vs Berry-Esseen

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#probability-theory #central-limit-theorem #probability-limit-theorems #large-deviation-theory
490
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A central limit theorem example.

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#probability #probability-theory #central-limit-theorem
144
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Central Limit Theorem Question Relating to Sample Mean

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#probability #normal-distribution #central-limit-theorem
87
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Central limit theorem for distribution peak rather than mean

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#probability #statistics #central-limit-theorem

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