List questions from probability-limit-theorems

Published on 24 May 2020 - 11:08

54

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Does the convergence in probability imply the following limit is $1?$

Published on 29 May 2020 - 11:23

325

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Weak convergence result in Levy's Continuity Theorem

Published on 30 May 2020 - 10:25

31

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Question about random variables convergence

Published on 05 Jun 2020 - 13:38

42

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if $\bar{X}\overset{p}{\rightarrow} \mu$ then $f(\bar{X})\overset{p}{\rightarrow} f(\mu)$?

Published on 05 Jun 2020 - 20:34

409

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Multinomial distribution converges to multiple Poisson distribution

Published on 07 Jun 2020 - 2:01

32

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Built a sequence

Published on 07 Jun 2020 - 10:54

74

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Proving a version of a local limit theorem

Published on 07 Jun 2020 - 12:49

95

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Probability for a biased die

Published on 10 Jun 2020 - 9:42

1.4k

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Let $\{X_n\}$ be i.i.d $N(0,1)$ random variables. Show that $\limsup_{n\rightarrow\infty} \frac{|X_n|}{\sqrt{\log n}}=\sqrt2$ a.s.

Published on 10 Jun 2020 - 15:54

787

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Chebyshev's Inequality Produces Result with Negative Value

Published on 11 Jun 2020 - 10:42

364

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Does $\sqrt{2\pi n} P(S_n =k)\to \exp(-x^2/2)$?

Published on 12 Jun 2020 - 6:01

703

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$X_n$ converges in distr. to $0$, $Y_n$ converges in prob. to $Y$. Show that $g(X_n,Y_n)$ converges in probability to $g(0,Y)$.

Published on 13 Jun 2020 - 17:09

162

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Show that $Y_n $ converges in distribution when suitably normalized

Published on 14 Jun 2020 - 19:27

87

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Normal Approximation to the Negative Hypergeometric Distribution

Published on 14 Jun 2020 - 19:45

List Question

If densities converge then the corresponding RV converge in distribution

Does the convergence in probability imply the following limit is $1?$

Weak convergence result in Levy's Continuity Theorem

Question about random variables convergence

if $\bar{X}\overset{p}{\rightarrow} \mu$ then $f(\bar{X})\overset{p}{\rightarrow} f(\mu)$?

Multinomial distribution converges to multiple Poisson distribution

Built a sequence

Proving a version of a local limit theorem

Probability for a biased die

Let $\{X_n\}$ be i.i.d $N(0,1)$ random variables. Show that $\limsup_{n\rightarrow\infty} \frac{|X_n|}{\sqrt{\log n}}=\sqrt2$ a.s.

Chebyshev's Inequality Produces Result with Negative Value

Does $\sqrt{2\pi n} P(S_n =k)\to \exp(-x^2/2)$?

$X_n$ converges in distr. to $0$, $Y_n$ converges in prob. to $Y$. Show that $g(X_n,Y_n)$ converges in probability to $g(0,Y)$.

Show that $Y_n $ converges in distribution when suitably normalized

Normal Approximation to the Negative Hypergeometric Distribution

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