# Tagged Questions

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### Co-occurrence Poisson binomial distribution

I'm using a Poisson binomial distribution for co-occurrence testing. I've 2 variables : X ~ Binom(px,n) and Y ~ Binom(py,n) (px and py are the probabilities, and both variable have the same number of ...
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### Probability Generating Function of Poisson Distribution

I was just wondering if someone could help me understand this derivation of the probability generating function for a Poisson distribution, (I understand it, until the last step): ...
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### Approach to a Poisson question

This is a question from an old test, taken completely out of context: "The customers arrive at a shop according to a Poisson distribution with mean $\lambda$ per hour. Each customer takes $1/k$ ...
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### Poisson distribution vs multiplying probabilities

I am a TA for a stats course for engineers, and I had a really good question from a student today, which I don't know the answer to. We were going through the following word problem: "4 computers ...
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### How to derive the probability mass function for Zero-inflated Poisson Distribution?

I am a maths student and I asked to derive the zero-inflated poisson distributon. I looked it up in the interent and I found the p.m.f. however I have no-idea why it looks the way it looks. Thank you ...
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### What is the probability of an occurrence within an interval

I am having an issue getting my head around this question as well. Gale-force winds occur on the average of 0.7 times every 54 hours. For an interval of 110 hours whats the probability r = 2? I ...
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### Probability of events

Here is a probability problem: you observe .5 cars on average passing in front of you every 5 minutes on a road. What is the probability of seeing at least 1 car in 10 minutes? I'm trying to solve ...
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### Problem reconciling exact and inexact Poisson distribution algorithms

I've written some code to calculate Poisson confidence limits (a) using Chi-squared, and (b) from first principles, using Poisson's probability mass function equation. However, the two sets of results ...
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### Calculating Total Probabilities from a Poisson Random Variable

First time post and I'm not sure if I'm posting in the right place but here goes: I enjoy Sports and was reading a book over Christmas (Mathletics by Wayne Winston) and to cut a long story short have ...
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### Error count limit for known residual failure rate and desired false-positive rate?

We perform a known fixed number $K$ of independent experiments, each of which has known/assumed residual odds $p$ to fail. We count the number $N$ of failures. How can I choose $M$ so that $N>M$ ...
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### How to derive Poisson distribution from gamma distribution?

Let $T_1, T_2, \dots$ be iid sequence of exponential random variables with parameter $\lambda$. The sum $S_n = T_1 + T_2 + \dots + T_n$ is a Gamma distribution. Now as I understand the Poisson ...
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### How do you solve a Poisson process problem

During an article revision the authors found, in average, 1.6 errors by page. Assuming the errors happen randomly following a Poisson process, what is the probability of finding 5 errors in 3 ...