Question

Why does $y \int_0^\infty x^2 e^{-y|x|} \, dx=\frac 1 {y^2}\int_0^\infty x^2 e^{-x}\,dx$?

score 78 · Answer 1 · 2026-03-26 01:10:39

78

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Why does $y \int_0^\infty x^2 e^{-y|x|} \, dx=\frac 1 {y^2}\int_0^\infty x^2 e^{-x}\,dx$?

Published on 26 Mar 2026 - 1:10

score 689 · Answer 2 · 2018-03-31 00:13:03

689

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Simplification PDF of maximum of Exponential random variable and find his Invers

Published on 31 Mar 2018 - 0:13

score 71 · Answer 3 · 2018-03-31 02:25:41

71

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Does the series $\sum_{i=1}^{\infty} \frac{X_i}{3^i}$ converge almost surely?

Published on 31 Mar 2018 - 2:25

score 447 · Answer 4 · 2018-03-31 03:57:53

447

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Basic example of $\sigma$-algebra generated by a random variable

Published on 31 Mar 2018 - 3:57

score 218 · Answer 5 · 2026-03-25 02:56:52

218

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Bivariate Normal

Published on 25 Mar 2026 - 2:56

score 28 · Answer 6 · 2018-03-31 13:04:52

28

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which law of probability is used in the following derivation

Published on 31 Mar 2018 - 13:04

score 48 · Answer 7 · 2018-04-01 06:29:22

Prove that $\displaystyle \lim_{n \to \infty}\mathbb E(e^{iuX_n})=\lim_{n \to\infty}\mathbb E(e^{iuX})$ where $X$ is the mean square limit of $X_n$

score 1k · Answer 8 · 2026-03-25 22:10:01

1k

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Convergence of Poisson random variables with divergent parameter

Published on 25 Mar 2026 - 22:10

score 438 · Answer 9 · 2026-03-27 04:45:28

438

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Almost independent random variables?

Published on 27 Mar 2026 - 4:45

score 2.5k · Answer 10 · 2026-03-25 10:57:02

2.5k

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PDF of sum of random variables (with uniform distribution)

Published on 25 Mar 2026 - 10:57

score 58 · Answer 11 · 2026-03-26 01:12:47

58

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Sequence of R.V.s $z_1, z_2, ...$ s.t. $P(z_i=1)=P(z_i=-1)=\frac 1 2$ converge almost surely?

Published on 26 Mar 2026 - 1:12

score 71 · Answer 12 · 2026-03-26 01:12:16

71

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Does $\max_{i\le n} \big|Z_i\big|=\frac 1 n \sum_{i\le n} \big|Z_i\big|$ as $n \to \infty$? (Convergence of R.V.s sequence $Z_1,Z_2,Z_3,...$)

Published on 26 Mar 2026 - 1:12

score 693 · Answer 13 · 2018-04-03 10:33:17

693

Views

Problem: Roll two dice and find the pmf of X

Published on 03 Apr 2018 - 10:33

score 37 · Answer 14 · 2026-03-25 01:13:18

37

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Random variables expectation

Published on 25 Mar 2026 - 1:13

score 2.9k · Answer 15 · 2018-04-03 14:40:28

2.9k

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Roll two dice, find the pmf of X if X is the difference between largest and smallest number

Published on 03 Apr 2018 - 14:40

List Question

Why does $y \int_0^\infty x^2 e^{-y|x|} \, dx=\frac 1 {y^2}\int_0^\infty x^2 e^{-x}\,dx$?

Simplification PDF of maximum of Exponential random variable and find his Invers

Does the series $\sum_{i=1}^{\infty} \frac{X_i}{3^i}$ converge almost surely?

Basic example of $\sigma$-algebra generated by a random variable

Bivariate Normal

which law of probability is used in the following derivation

Prove that $\displaystyle \lim_{n \to \infty}\mathbb E(e^{iuX_n})=\lim_{n \to\infty}\mathbb E(e^{iuX})$ where $X$ is the mean square limit of $X_n$

Convergence of Poisson random variables with divergent parameter

Almost independent random variables?

PDF of sum of random variables (with uniform distribution)

Sequence of R.V.s $z_1, z_2, ...$ s.t. $P(z_i=1)=P(z_i=-1)=\frac 1 2$ converge almost surely?

Does $\max_{i\le n} \big|Z_i\big|=\frac 1 n \sum_{i\le n} \big|Z_i\big|$ as $n \to \infty$? (Convergence of R.V.s sequence $Z_1,Z_2,Z_3,...$)

Problem: Roll two dice and find the pmf of X

Random variables expectation

Roll two dice, find the pmf of X if X is the difference between largest and smallest number

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