List questions from almost-everywhere

Published on 20 May 2020 - 20:45

62

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a.e-defined integrable functions

Published on 23 May 2020 - 4:44

203

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Proving $\sum_{k=1}^\infty \rightarrow -\infty$ almost surely if $P(X_k=k^2)=\frac{1}{k^2}=p_k, P(X_k=-1)=1-p_k$.

Published on 28 May 2020 - 6:30

304

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Almost sure convergence of a sum of independent r.v

Published on 28 May 2020 - 9:22

120

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If $\int_E f\,d\mu=\int_E g\,d\mu$ then $f=g$ a.e?

Published on 30 May 2020 - 18:54

149

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Proving $\operatorname{cos}(x+y)=\operatorname{cos}(x)\operatorname{cos}(y)-\operatorname{sin}(x)\operatorname{sin}(y)$ using differentiation

Published on 31 May 2020 - 4:02

90

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Show that $\log{M_n}/\log{n}\to1$ a.s. where $M_n = \max\{X_k \mid 1 \leq k \leq n\}$ and the $X_n$ are iid with $\mathbb{P}(X_n \geq i) = 1/i$.

Published on 04 Jun 2020 - 15:22

54

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Sufficient condtions for almost sure convergence - proof verification

Published on 20 Jun 2020 - 21:28

156

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Almost sure convergence with Pareto distribution

Published on 22 Jun 2020 - 14:35

807

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Introduction to $L^2$ space. Equivalence class concept

Published on 29 Jun 2020 - 10:29

167

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Law of Large Numbers when expectation is infinite and random variable not identical

Published on 01 Jul 2020 - 4:15

144

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Proving a variant of the Kolmogorov SLLN

Published on 07 Jul 2020 - 0:47

109

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Comparing elements of $L^p$ spaces

Published on 16 Jul 2020 - 9:29

135

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Implications of an expected value on almost sure convergence

Published on 20 Jul 2020 - 23:16

76

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Proof that $ \sum_{i=1}^\infty a_n$ is converges almost surely.

Published on 22 Jul 2016 - 10:59

List Question

Almost sure and expectation. How are they exactly related?

a.e-defined integrable functions

Proving $\sum_{k=1}^\infty \rightarrow -\infty$ almost surely if $P(X_k=k^2)=\frac{1}{k^2}=p_k, P(X_k=-1)=1-p_k$.

Almost sure convergence of a sum of independent r.v

If $\int_E f\,d\mu=\int_E g\,d\mu$ then $f=g$ a.e?

Proving $\operatorname{cos}(x+y)=\operatorname{cos}(x)\operatorname{cos}(y)-\operatorname{sin}(x)\operatorname{sin}(y)$ using differentiation

Show that $\log{M_n}/\log{n}\to1$ a.s. where $M_n = \max\{X_k \mid 1 \leq k \leq n\}$ and the $X_n$ are iid with $\mathbb{P}(X_n \geq i) = 1/i$.

Sufficient condtions for almost sure convergence - proof verification

Almost sure convergence with Pareto distribution

Introduction to $L^2$ space. Equivalence class concept

Law of Large Numbers when expectation is infinite and random variable not identical

Proving a variant of the Kolmogorov SLLN

Comparing elements of $L^p$ spaces

Implications of an expected value on almost sure convergence

Proof that $ \sum_{i=1}^\infty a_n$ is converges almost surely.

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