Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [poisson-distribution]

For questions relating to Poisson distributions in probability theory. To be used with [probability] or [probability-distributions] tag.

The PMF of a random variable $X$ distributed according to the Poisson distribution with parameter $\lambda > 0$ is the following: $$\Pr\left[X=k\right]=\frac{\lambda^k \exp(-\lambda)}{k!}\;,\; k\geq 0$$ This distribution describes the number of independent events occurring with constant rate in some unit time, the average being $\lambda$ events per unit.

2416 questions
0
votes
1 answer

Using $X$ in Poisson distributions

Suppose the number of, lets say flowers, are distributed randomly in a field of $1120$ sq. meters. If there are $96$ flowers in this field, then the mean is $96/1120$ for a Poisson distribution. Assuming this if we chose a random area of $20$ sq.…
Olivetti
  • 3
0
votes
2 answers

Poisson distribution independent events

I am going to write my solution upon an earlier suggestion made on this Poisson distribution problem, I would appreciate if someone could tell me if it is correct: Number of physics problems that Mike tries for any given week follows a Poisson…
Aurora Borealis
  • 1,747
0
votes
1 answer

Maximum likelihood estimate of the parameter in Poisson distribution

Given that the number of goals scored per match by a football team can be assumed to be a Poisson random variable with mean $\theta$. In eight games, the team scores 3, 6, 2, 5, 4, 1, 4, 5 goals. (a) Let $X$ that follows a Poisson distribution with…
steve mike
  • 43
0
votes
1 answer

showing independence of Poisson distribution

I was doing some past exams on distributions, and I can not do part e), nor do I understand the mark scheme. The first 4 questions I did as workings below, but can anyone help me try to understand and show part e)?
Aurora Borealis
  • 1,747
0
votes
0 answers

How to solve this Poisson-distribution question?

The weight of certain type of muffin is approximately 50 grams. Let X be the number of muffins that weigh more than 50 grams has the probability of 0.005. A sample of 100 muffins are selected randomly. Show that the distribution of muffin that…
Eizaz Aqil
  • 1
0
votes
1 answer

On a Poisson distribution

Here is the Question I'm stuck on: A petrol station has service areas on both sides of a motorway, one to serve north-bound traffic and the other for south-bound traffic. The number of north— bound vehicles arriving at the station in one minute has a…
Iliass Gamer
  • 11
  • 1
0
votes
1 answer

how to use Poisson approximation on this problem

suppose you and I each have a box of 600 marbles. In my box, 4 of the marbles are black, while 3 of your marbles are black. we each draw 300 marbles with replacement from our own boxes.Approximately, what's the chance that you and I draw the same…
Shirley Yan
  • 1
0
votes
1 answer

Poisson Distribution with conditional probability

Let a fisherman catch fish like a Poisson process s with known catching intensity λ=2 per 90 minutes. The amount of fish caught at minute $t ∈ [0,90], s(t)$ is then Poisson distributed with expected value $E[s(t)]=\frac{tλ}{90},t ∈ [0,90]$. The…
Cruceru Vlad
  • 1
0
votes
0 answers

Reversing a Poisson formula

I am attempting to create a formula that takes the decimal odds of there being under 2.5 goals in a soccer match, and returns the estimated number of goals based on this. So far though, I have only been able to do the opposite - when the estimated…
Matt
  • 11
0
votes
1 answer

Poisson distribution, and embedded poisson distribution

Assume that $X_j$ and $Y_j$ are both independent poisson distributed RV with the same rate $\lambda>0$ for all $j=0,1,2,....$. Now define $U_j$ such that $U_j(\omega)=Y_{X_{j}(\omega)}(\omega)$ for all $\omega \in \Omega$. I now want to find…
Jonathan Kiersch
  • 365
0
votes
2 answers

a statistical question which i thought it was a binomial distribution

A mathematics textbook has 100 pages on which typographical errors in the equations could occur. Suppose there are in fact two pages with errors. What is the probability that a random sample of 20 pages will contain at least one error? read some…
yts61
  • 103
0
votes
1 answer

Request arrival following Poisson distribution

I have difficulty understanding how to use Poisson to represent request arrival rate to a server. Let's say I collected the number of requests coming in to a server every hour. At a certain hour, the server receives 30000 requests per hour. Then I…
cathy305
  • 1
0
votes
0 answers

Expected value and variance of expected value for a poisson process

The number of arrivals at a customer information desk is 2 per minute. Assuming the number of arrivals follows a poisson distribution, find (a) the expected number of arrivals in 3 minutes and (b) the variance of the number of enquiries arriving in…
Sjoseph
  • 269
0
votes
2 answers

Expected value of geometric mean of Poisson random variables

I am interested in trying find the expected value of the geometric mean of a set of i.i.d. Poisson random variables. Say we have $Y_1,\dots,Y_n$, where $$Y_i \sim Poisson(\lambda) $$ Then, the geometric mean can be expressed as: $$…
Ryan Simmons
  • 127
0
votes
0 answers

Poisson Distribution question solving

I'm stuck solving a Poisson distribution question, not entirely sure how I go about actually calculating the answer So a call centre receives telephone calls at a rate of 12 per hour, the clerk working at the centre wants to go for a break. How long…
daenwaels
  • 11
1 2 3 4
5
6 7