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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.

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Why does the Poisson distribution have a left skewness

The Poisson distribution can be interpreted as a propability distribution that returns how likely it is that a certain number of events will occur, when the mean is known. Regardless it's formula, whats the the intuition behind the shape of that…
Pluxyy
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Find probability with the help of Poisson distribution

There are $3$ cyclone on average in a year in russia . What is the probability that there will be cyclone in the next TWO years ? I just want to know the value of $\lambda$ in Poisson distribution! As we know $\lambda$ actually works on the same…
Schl....r
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Find the distribution of a sum of Poisson random variable

Let $X_1,X_2,..,X_N$ be independent identical samples from a Poission distribution with unknown parameter $\theta$ How would I find the sum of the distribution $X_1+X_2+X_3+..+X_N$ when n is finite. I looked up convolution but that only works for…
Fernando Martinez
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Let N be a poisson random variable with parameter µ, and conditional on N, let M have a binomial distribution with parameters N and p. Then...

https://i.gyazo.com/3f6b7a71c5d32fa7c309a2e959610480.png Help me understand what happens from line 2 to line 3. What rules are applied?
Sebastian Nielsen
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Generation distribution for Poisson offspring

If a certain animal has $N$ offspring, with $N$ Poisson distributed, what is the distribution of $Z$, the surviving offspring in the next generation (each offspring has probability p of surviving)? I found online theory about Poisson branching…
CalcBoy
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Poisson Probability Question -Please help

Can you please help me on this question The number of fishes caught by a fisherman is Poisson with an average of $6$ fishes per hour, assume he caught $8$ fishes in the last hour, what is the probability of no fish was caught in the first $10$…
Mary
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Poisson Question Derivation

How is the second last line obtained from the line before it?
user672518
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May I know how to exclude tied rank, and interpret the sum of the Poisson random variables?

for the first part of the question, my interpretation is that: So, there are two tied ranks, so I should delete them from the data set? For the second part of the question, I want to ask how do I interpret the fact that the sum of independent…
Henry Cai
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What is the use of the poisson distribution in this exercise when the question seems to have no relation

In one exercise they give me 1) The probability function of having k failures in a machine: $$P_k=\dfrac{1}{ek!}\\$$ where $$k=1,2,3,... (infinity)\\$$ 2) The probability that the machine stop working having k failures:…
Limanido
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Question about multiple poisson distributions

Suppose $X_1, X_2, X_3, ...X_n$ ~iid Poisson(3), and $\bar{X}_m = (X_1+X_2+X_3+...+X_m)/m$, $\bar{X}_m$ being the mean of the first m terms of X. a. Find the exact value of $P(2.6<=\bar{X}_2<=3.1)$ b. Estimate $P(2.6<=\bar{X}_{50}<=3.1)$
J zeigler
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Question about poisson and probability/exponential distribution

I'm a little confused about this question I was given: "Calls arrive at a tech support center with a mean of 4 per hour. Assuming the number of calls received in 1hr is described by a Poisson distribution, find the probability that there is more…
Dog with a stick
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Let X be a random variable with a Poisson distribution, such that P(X > 2) = 0.3. Find P (X < 2).

The question is: Let X be a random variable with a Poisson distribution, such that P(X > 2) = 0.3. Find P (X < 2). So, my workings so far are in line with the answer booklet but then the booklet goes; $$e^{-\lambda}[1+\lambda + \frac{\lambda^2}{2}…
Ernie Stewards
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Poisson variables comparisons in log-concavity, dispersive order

Let X be a Poisson variable with parameter λ with a probability mass function, f(k), where k = 0, 1, 2 … We know the index of log-concavity is the function rf(k) = f(k)^2/(f(k-1)f(k+1) = (k+1)/k>1. So, Poisson is log-concave. Many books have: "The…
Simon
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How to use Poisson distribution on this task

The ferry crosses the strait from beach A to beach B at regular intervals of 20 minutes. The ferry has room for 7 cars. Suppose no cars left behind when ferry first leave. Suppose the number of cars arriving on the beach A the next 20 minutes in the…
pokeri
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Poisson distribution : number of failures during a particular week

I've this issue with this Poisson distribution. I need to calculate the probability that there will not be more than one failure during a particular week. Given electricity power failures occur according to a Poisson distribution with an average of…
Carlos Carvalho
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