Question

Show that random variable $U=\frac{X}{X+Y}$ has uniform distribution on [0,1] when X & Y are independent random variables with same exp. distribution.

score 737 · Answer 1 · 2020-06-16 17:06:12

737

Views

Show that random variable $U=\frac{X}{X+Y}$ has uniform distribution on [0,1] when X & Y are independent random variables with same exp. distribution.

Published on 16 Jun 2020 - 17:06

score 108 · Answer 2 · 2020-06-16 17:54:39

108

Views

Mittag-Leffler function for $x$ big

Published on 16 Jun 2020 - 17:54

score 419 · Answer 3 · 2020-06-16 19:33:28

419

Views

Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution

Published on 16 Jun 2020 - 19:33

score 800 · Answer 4 · 2020-06-16 21:41:35

800

Views

Minimum of exponential random variable

Published on 16 Jun 2020 - 21:41

score 546 · Answer 5 · 2020-06-17 18:36:22

546

Views

3 Probability Questions: Exponential distribution and Normal

Published on 17 Jun 2020 - 18:36

score 41 · Answer 6 · 2020-06-17 23:04:24

41

Views

What is $E\left(\lceil X\rceil\right)$ when $X$ is exponential?

Published on 17 Jun 2020 - 23:04

score 134 · Answer 7 · 2020-06-18 11:50:53

134

Views

How to find unbiased estimator which is based on maximum likelihood for this problem?

Published on 18 Jun 2020 - 11:50

score 156 · Answer 8 · 2020-06-20 20:19:48

156

Views

Belief updating on censored exponential distribution

Published on 20 Jun 2020 - 20:19

score 118 · Answer 9 · 2026-03-25 17:37:20

118

Views

Distribution function of $Y = \max\{X \sim \text{Exp}(2), 3\}$

Published on 25 Mar 2026 - 17:37

score 90 · Answer 10 · 2020-06-25 01:27:59

90

Views

Examining $\Pr(Y_u - X_u > z)$ where $X_u,Y_u$ are sample means of independent exponential variables

Published on 25 Jun 2020 - 1:27

score 361 · Answer 11 · 2020-06-26 17:14:31

361

Views

If $X$ follows an $\operatorname{Exp}(\theta)$, does $1/X$ follow an $\operatorname{Exp}(1/ \theta)$?

Published on 26 Jun 2020 - 17:14

score 69 · Answer 12 · 2020-06-27 23:27:05

69

Views

Messing up sum of two random variables with the same exponential distribution.

Published on 27 Jun 2020 - 23:27

score 537 · Answer 13 · 2020-06-29 01:51:45

537

Views

UMVUE and complete sufficient statistic

Published on 29 Jun 2020 - 1:51

score 163 · Answer 14 · 2026-03-25 17:16:55

163

Views

If $X$ is exponential distributed with parameter $\lambda$, how is $\bar{X}/\lambda$ distributed?

Published on 25 Mar 2026 - 17:16

score 204 · Answer 15 · 2026-03-25 17:37:41

204

Views

What base does the author take when taking the log of both sides?

Published on 25 Mar 2026 - 17:37

List Question

Show that random variable $U=\frac{X}{X+Y}$ has uniform distribution on [0,1] when X & Y are independent random variables with same exp. distribution.

Mittag-Leffler function for $x$ big

Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution

Minimum of exponential random variable

3 Probability Questions: Exponential distribution and Normal

What is $E\left(\lceil X\rceil\right)$ when $X$ is exponential?

How to find unbiased estimator which is based on maximum likelihood for this problem?

Belief updating on censored exponential distribution

Distribution function of $Y = \max\{X \sim \text{Exp}(2), 3\}$

Examining $\Pr(Y_u - X_u > z)$ where $X_u,Y_u$ are sample means of independent exponential variables

If $X$ follows an $\operatorname{Exp}(\theta)$, does $1/X$ follow an $\operatorname{Exp}(1/ \theta)$?

Messing up sum of two random variables with the same exponential distribution.

UMVUE and complete sufficient statistic

If $X$ is exponential distributed with parameter $\lambda$, how is $\bar{X}/\lambda$ distributed?

What base does the author take when taking the log of both sides?

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