List questions from probability-limit-theorems

Published on 15 Jun 2020 - 8:16

60

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Where does this equality come?

Published on 17 Jun 2020 - 12:38

89

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Doubt on strong law of large number theorem

Published on 17 Jun 2020 - 13:37

265

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Show that if $\phi_{X}(t)=1$ in a neighborhood of $0$, then $X=0$ a.s.

Published on 17 Jun 2020 - 21:13

249

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Use Slutsky's theorem to show that: $\sqrt{n}(e^{\frac{S_n}{n}}-e^{\mu}) \xrightarrow{d} \sigma e^{\mu}Z$

Published on 18 Jun 2020 - 0:31

62

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Can i use L’Hopital’s rule $f(x)\left[ {\mathop {\lim }\limits_{x \to 0} \frac{{g(x)}}{{h(x)}}} \right]$?

Published on 18 Jun 2020 - 1:18

810

Views

Probability that a book with $200$ pages has $3$ misprints at most using Poisson approximation

Published on 19 Jun 2020 - 3:51

22

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Came across this question while practising for Central Limit Theorem

Published on 20 Jun 2020 - 10:20

119

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For two vectors in $\{\pm1\}^n$, take the probability that the ratio of their overlap and $\sqrt{n}$ is less than some integer $M$ then take its limit

Published on 20 Jun 2020 - 15:50

503

Views

zero-one-law in percolation theory

Published on 26 Mar 2026 - 6:12

261

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Central limit theorem with a biased dice

Published on 24 Jun 2020 - 22:45

93

Views

Combine two Taylor expansions (Lindeberg CLT)

Published on 27 Jun 2020 - 18:01

100

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Show that $\frac{S_n - \mathbb{E}S_n}{\sigma \sqrt{n}} \to \mathcal{N}(0,1)$ in distribution.

Published on 01 Jul 2020 - 0:15

554

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Covariance between functions of random variables

Published on 01 Jul 2020 - 11:39

194

Views

Markov chain conditional limit

Published on 02 Jul 2020 - 19:34

List Question

Lindeberg and Lyapunov's condition on symmetric bernoulli random variables

Where does this equality come?

Doubt on strong law of large number theorem

Show that if $\phi_{X}(t)=1$ in a neighborhood of $0$, then $X=0$ a.s.

Use Slutsky's theorem to show that: $\sqrt{n}(e^{\frac{S_n}{n}}-e^{\mu}) \xrightarrow{d} \sigma e^{\mu}Z$

Can i use L’Hopital’s rule $f(x)\left[ {\mathop {\lim }\limits_{x \to 0} \frac{{g(x)}}{{h(x)}}} \right]$?

Probability that a book with $200$ pages has $3$ misprints at most using Poisson approximation

Came across this question while practising for Central Limit Theorem

For two vectors in $\{\pm1\}^n$, take the probability that the ratio of their overlap and $\sqrt{n}$ is less than some integer $M$ then take its limit

zero-one-law in percolation theory

Central limit theorem with a biased dice

Combine two Taylor expansions (Lindeberg CLT)

Show that $\frac{S_n - \mathbb{E}S_n}{\sigma \sqrt{n}} \to \mathcal{N}(0,1)$ in distribution.

Covariance between functions of random variables

Markov chain conditional limit

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