List questions from poisson-distribution

Published on 12 Aug 2020 - 4:12

110

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Find UMVUE of $P(X_1+X_2+X_3 =2)$ Where $X_1, ... X_n \sim$ Poisson$(\lambda)$ (independent)

Published on 02 Apr 2026 - 3:17

208

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Probability Poisson random variable is larger than Exponential random variable

Published on 30 Mar 2026 - 15:35

147

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When you can look through a forest?

Published on 15 Aug 2020 - 8:06

67

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Let $X\sim \pi(\lambda)$, find $E\Bigl[\frac{1}{(X+1)}\Bigr]$.

Published on 16 Aug 2020 - 9:55

1.4k

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Arrival of customers at shop ~ Poisson. What is the probability that a single customer arrive in 1/4 of the time?

Published on 04 Apr 2026 - 7:05

271

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Expected number of pages read

Published on 17 Aug 2020 - 12:28

1.2k

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Poisson process conditional distribution

Published on 18 Aug 2020 - 10:52

84

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Find probability that arrived claim is type 1 and probability this claim has size larger than 1.

Published on 30 Mar 2026 - 15:34

115

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Show that ${{n}\choose{x}}p_n^x(1-p_n)^{n-x}=e^{-\lambda}\frac{\lambda^x}{x!}$

Published on 02 Apr 2026 - 15:12

988

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Sum of two Poisson random variables

Published on 21 Aug 2020 - 14:31

409

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What's the marginal distribution for the compound beta-binomial distribution conditioned on a poisson random variable?

Published on 26 Mar 2026 - 11:06

487

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Characteristic function of $Z=X-Y$, where $X$ and $Y$ follows Po($\lambda$) and prove that $E[Z^2]=2\lambda$

Published on 31 Mar 2026 - 21:54

227

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The posterior distribution of the Poisson-Gamma Model

Published on 26 Mar 2026 - 21:09

38

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Prove that these conditions are equivalent

Published on 02 Apr 2026 - 15:23

List Question

Sum of Poissons is Poisson with adding parameters

Find UMVUE of $P(X_1+X_2+X_3 =2)$ Where $X_1, ... X_n \sim$ Poisson$(\lambda)$ (independent)

Probability Poisson random variable is larger than Exponential random variable

When you can look through a forest?

Let $X\sim \pi(\lambda)$, find $E\Bigl[\frac{1}{(X+1)}\Bigr]$.

Arrival of customers at shop ~ Poisson. What is the probability that a single customer arrive in 1/4 of the time?

Expected number of pages read

Poisson process conditional distribution

Find probability that arrived claim is type 1 and probability this claim has size larger than 1.

Show that ${{n}\choose{x}}p_n^x(1-p_n)^{n-x}=e^{-\lambda}\frac{\lambda^x}{x!}$

Sum of two Poisson random variables

What's the marginal distribution for the compound beta-binomial distribution conditioned on a poisson random variable?

Characteristic function of $Z=X-Y$, where $X$ and $Y$ follows Po($\lambda$) and prove that $E[Z^2]=2\lambda$

The posterior distribution of the Poisson-Gamma Model

Prove that these conditions are equivalent

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