List questions from exponential-distribution

Published on 25 Apr 2021 - 19:56

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What is the cumulative distribution function of T?

Published on 27 Mar 2026 - 15:18

99

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$Z_i=X_i-Y_i$ with $X_i$ and $Y_i$ independent and exponentially distributed

Published on 27 Apr 2021 - 10:21

43

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understanding the convolution of random variable formula

Published on 27 Mar 2026 - 4:15

117

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Moment estimator and its asymptotic distribution for exponential distribution

Published on 28 Apr 2021 - 21:15

88

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$\tilde{F}_X(s) = E\left( e^{-sX} \right) = \int_0^\infty e^{-sx} f_X(x) \ dx = \frac{\lambda}{\lambda + s} \,, \ \text{Re}(s) > - \lambda$?

Published on 29 Apr 2021 - 18:05

48

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Finding $E(X\cdot\mathbb{1}_{X\ge t}\mid Y_{t})$ where $X\sim\text{Exp}(\lambda)$ and $Y_{t}=\min(t,X)$

Published on 30 Apr 2021 - 17:09

1.5k

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Memoryless property: how does $P(X > s + t \mid X > s) = P(X > t), s, t \ge 0$ imply that $F^c(s + t) = F^c(s) F^c(t), s, t \ge 0$?

Published on 27 Mar 2026 - 15:20

129

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Probability distribution for number of concurrent events

Published on 04 May 2021 - 2:30

176

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Find $E(X_{(1)}\mid T)$ where $T=\sum_{i=1}^n X_i$

Published on 30 Mar 2026 - 10:19

404

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Let $X$~$U(0,5)$ & $Y$ be exponential random variable with with mean $2x$. Find the mean and variance of Y.

Published on 06 May 2021 - 7:04

78

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Find the joint distribution and covariance with exponential density

Published on 26 Mar 2026 - 14:20

69

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An argument on exponential distribution

Published on 09 May 2021 - 8:20

161

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The distribution of an event whose waiting time is exactly k

Published on 09 May 2021 - 13:01

315

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Proving Transformation of Random Variable is Chi-Square with 2 Degrees of Freedom

Published on 27 Mar 2026 - 21:37

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Most Powerful test for deciding distribution

What is the cumulative distribution function of T?

$Z_i=X_i-Y_i$ with $X_i$ and $Y_i$ independent and exponentially distributed

understanding the convolution of random variable formula

Moment estimator and its asymptotic distribution for exponential distribution

$\tilde{F}_X(s) = E\left( e^{-sX} \right) = \int_0^\infty e^{-sx} f_X(x) \ dx = \frac{\lambda}{\lambda + s} \,, \ \text{Re}(s) > - \lambda$?

Finding $E(X\cdot\mathbb{1}_{X\ge t}\mid Y_{t})$ where $X\sim\text{Exp}(\lambda)$ and $Y_{t}=\min(t,X)$

Memoryless property: how does $P(X > s + t \mid X > s) = P(X > t), s, t \ge 0$ imply that $F^c(s + t) = F^c(s) F^c(t), s, t \ge 0$?

Probability distribution for number of concurrent events

Find $E(X_{(1)}\mid T)$ where $T=\sum_{i=1}^n X_i$

Let $X$~$U(0,5)$ & $Y$ be exponential random variable with with mean $2x$. Find the mean and variance of Y.

Find the joint distribution and covariance with exponential density

An argument on exponential distribution

The distribution of an event whose waiting time is exactly k

Proving Transformation of Random Variable is Chi-Square with 2 Degrees of Freedom

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