Tagged Questions

0
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0answers
50 views

Distribution of independent binomial variables conditional upon the sum

Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
0
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0answers
27 views

Optimizing a Poisson Process

So, I was standing in line for a Paramore concert for a very long time this past weekend because the boyfriend wanted to be up front during the show. I got to thinking, what would be the optimal time ...
1
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0answers
26 views

Markov chain from Poisson: null or positive recurrent?

Let $K_t$ be a Poisson process with rate $1$ and $X_n=K_n-n$ $, \ \ \ n\in \mathbb{N}$ Now I want to determine whether it is null or positive recurrent, we already know it is recurrent. I ...
0
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0answers
116 views

Bivariate Poisson - Cant seem to understand it. Could someone pls tell me how to work it out in laymans terms?

Researching bivariate poisson over the web is no easy task unless you can make sense of the greek symbols. I am familiar with poisson and have a deep understanding of it. So could someone explain ...
3
votes
1answer
496 views

How to calculate cumulative Poisson probabilities without adding each one if no. of outcomes is large and hence, adding (without excel) is difficult?

One can calculate the probability of a correct score of a football match by Poisson(Number of Team1 goals, Mean average Team1 goals) x Poisson(Number of Team2 goals, Mean average Team2 goals) So for ...
0
votes
2answers
247 views

Wigan scores after 30 minutes. Calculate home, away and draw in percentage terms with poisson regression

I have the following exercise: Wigan v city 90 mins match: Wigan scores after 30 minutes. Calculate home, away and draw in percentage terms with poisson regression, assuming pre-match odds ...
3
votes
1answer
146 views

Expectation and confidence intervals of a Poisson process

A Poisson process has PDF $$P(X=k)=\frac{e^{-\lambda t}(\lambda t)^k}{k!}$$ I'm trying to find an expression for: $E[X | \lambda, t]$ Confidence intervals (i.e. find $\delta$ such that ...
4
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0answers
118 views

Conditional probability update for correlated Poisson variables

Some background: I am trying to estimate the number of failures in two related machine populations. I model machine failures in a year as a correlated Poisson process as such: $Y_0,\ Y_1$ and $Y_2$ ...
1
vote
1answer
54 views

Finding variance?

$\newcommand{\Var}{\mathrm{Var}}$ Consider $Z_i$ as a binary random variable with $\mathrm{Pr}[Z_i = 1] = \pi$. Also, consider $Y_i$ as: $Y_i|Z_i = 0 \sim \mathrm{Poisson} (\lambda_0) $ $Y_i|Z_i = 1 ...
1
vote
0answers
130 views

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 ...
2
votes
1answer
78 views

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 ...
3
votes
1answer
149 views

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 ...
2
votes
2answers
233 views

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 ...
4
votes
1answer
557 views

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 ...
1
vote
1answer
69 views

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 $N>M$ ...
4
votes
1answer
1k views

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 ...
5
votes
2answers
945 views

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 ...
2
votes
1answer
140 views

Poisson process, time and probabilities

An average of n birds fly through an area, in an hour, following a Poisson process. (I think this means the hours don't matter; there's no influence in the number of birds that fly through, at ...
2
votes
2answers
212 views

What distribution should be used for the detection of out of shelf situations in a retail stores?

I need to detect Out Of Shelf situations in reatil stores. What I had in mind is to assume that purchase frequency of some article (SKU) has certain ditribution (I tried with Poisson) and then ...