Question

What density does $Z=\frac{a_n-\sum_{i=1}^n\xi_i}{\sqrt n}$, $\xi_i\sim\operatorname{Cauchy}(0,1)$, converge to?

score 79 · Answer 1 · 2026-04-01 08:06:45

79

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What density does $Z=\frac{a_n-\sum_{i=1}^n\xi_i}{\sqrt n}$, $\xi_i\sim\operatorname{Cauchy}(0,1)$, converge to?

Published on 01 Apr 2026 - 8:06

score 116 · Answer 2 · 2021-06-18 20:24:14

116

Views

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score 149 · Answer 3 · 2021-06-18 21:53:30

149

Views

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41

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201

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score 173 · Answer 6 · 2021-06-21 14:09:12

173

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score 1.5k · Answer 7 · 2021-06-22 12:45:16

1.5k

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Find $\operatorname{Pr}\left ( Y< 0.5\mid X< 0.5 \right )$ with the given joint probability density function

Published on 22 Jun 2021 - 12:45

score 34 · Answer 8 · 2021-06-23 07:24:24

34

Views

How do conditional densities look like when the base measure does not factorize?

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score 36 · Answer 9 · 2021-06-23 11:06:13

36

Views

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score 48 · Answer 10 · 2026-03-30 03:55:16

48

Views

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score 29 · Answer 11 · 2021-06-27 14:29:35

29

Views

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Published on 27 Jun 2021 - 14:29

score 64 · Answer 12 · 2021-06-28 13:01:53

64

Views

Find the conditional probability density function $f_{X -Y|XY}(x,y)$

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score 81 · Answer 13 · 2021-06-28 13:56:39

81

Views

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score 466 · Answer 14 · 2026-03-26 17:35:45

466

Views

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score 32 · Answer 15 · 2021-07-04 11:35:19

Density of $U$ and $V$ given density of $(U,V)$ with $\frac{1}{\sqrt{4\pi}}e^{-\frac{u^2}{4}}\frac{1}{\sqrt{4\pi}}e^{-\frac{v^2}{4}}$

List Question

What density does $Z=\frac{a_n-\sum_{i=1}^n\xi_i}{\sqrt n}$, $\xi_i\sim\operatorname{Cauchy}(0,1)$, converge to?

Differentiating probability measures to obtain density functions

Let's find solutions to two functional differential equations

How to show independence between two random variables that are not Gaussian

Density of a probability measure that is not absolutely continuous wrt Lebesgue measure

How to integrate $x \ln(x)$ over density of $x$?

Find $\operatorname{Pr}\left ( Y< 0.5\mid X< 0.5 \right )$ with the given joint probability density function

How do conditional densities look like when the base measure does not factorize?

Density of frog's distance to the center of the circle in the limit

Probability of Y, where $Y=X^2$ and $X \sim U[-1, 1]$

Where does the $\frac{1}{2}$ go/disappear when computing the law of this RV?

Find the conditional probability density function $f_{X -Y|XY}(x,y)$

Add Skew to Distribution without Changing mean or variance

Understanding marginal distribution along a projection.

Density of $U$ and $V$ given density of $(U,V)$ with $\frac{1}{\sqrt{4\pi}}e^{-\frac{u^2}{4}}\frac{1}{\sqrt{4\pi}}e^{-\frac{v^2}{4}}$

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