List questions from probability-limit-theorems

Published on 10 Apr 2026 - 10:33

247

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Proving almost sure convergence (help understanding a step in a proof)

Published on 10 May 2026 - 13:24

1.1k

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Convergence in distribution of Poisson variables.

Published on 10 May 2026 - 19:35

904

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Continuous Mapping Theorem with two sequences of random variables?

Published on 28 Mar 2026 - 2:05

75

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Delta Method when sequence might not converge

Published on 28 Mar 2026 - 4:38

74

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Upper bound for $\Pr(\sum_y x_k^2 a_k \leq c)$: ideas better than multivariate Chebyshev?

Published on 28 Mar 2026 - 4:27

668

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prove a function of sequence of random variables converges

Published on 27 Mar 2026 - 22:48

75

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$\frac 1n \sum_{k=c+1}^n X_k X_{k-c}$ converges a.s to $0$ when $X_n$ is i.i.d. with mean $0$.

Published on 28 Mar 2026 - 9:09

39

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limit of $c_n$ when $\sqrt{n}*(c_n - 1)$ converges to a real number $c$

Published on 28 Mar 2026 - 0:59

87

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How does the first moment affect convergence in distribution?

Published on 28 Mar 2026 - 13:29

1.6k

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poisson limit theorem for multinomial distribution

Published on 27 Mar 2026 - 17:58

73

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Show that $\sqrt{\sum_{i}^n X_i} - \sqrt{n} \to Y \sim \mathcal{N}(\mu, \sigma^2)$ in distribution.

Published on 28 Mar 2026 - 3:15

3.5k

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Limiting distribution of MLE for uniform distribution

Published on 28 Mar 2026 - 4:18

298

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Application of CLT for bounded random variables with slowly decreasing variance

Published on 27 Mar 2026 - 18:09

132

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Using the WLLN to find the limiting distribution of a random variable

Published on 27 Mar 2026 - 23:43

List Question

Limiting Poisson Process

Proving almost sure convergence (help understanding a step in a proof)

Convergence in distribution of Poisson variables.

Continuous Mapping Theorem with two sequences of random variables?

Delta Method when sequence might not converge

Upper bound for $\Pr(\sum_y x_k^2 a_k \leq c)$: ideas better than multivariate Chebyshev?

prove a function of sequence of random variables converges

$\frac 1n \sum_{k=c+1}^n X_k X_{k-c}$ converges a.s to $0$ when $X_n$ is i.i.d. with mean $0$.

limit of $c_n$ when $\sqrt{n}*(c_n - 1)$ converges to a real number $c$

How does the first moment affect convergence in distribution?

poisson limit theorem for multinomial distribution

Show that $\sqrt{\sum_{i}^n X_i} - \sqrt{n} \to Y \sim \mathcal{N}(\mu, \sigma^2)$ in distribution.

Limiting distribution of MLE for uniform distribution

Application of CLT for bounded random variables with slowly decreasing variance

Using the WLLN to find the limiting distribution of a random variable

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