# What is Poisson: Definition and 505 Discussions

In probability theory and statistics, the Poisson distribution (; French pronunciation: [pwasɔ̃]), named after French mathematician Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10. Another example is the number of decay events that occur from a radioactive source during a defined observation period.

View More On Wikipedia.org
1. ### A Poisson noise on ##a_{\ell m}## complex number: real or complex?

1) In a cosmology context, when I add a centered Poisson noise on ##a_{\ell m}## and I take the definition of a ##C_{\ell}## this way : ##C_{\ell}=\dfrac{1}{2\ell+1} \sum_{m=-\ell}^{+\ell} \left(a_{\ell m}+\bar{a}_{\ell m}^{p}\right)\left(a_{\ell m}+\bar{a}_{\ell m}^{p}\right)^* ## Is Poisson...

16. ### Solving the Poisson equation

I tried to follow the method outlined in lectures, and ended up with an incorrect solution. My understanding of PDEs is a bit shaky so I thank anyone for constructive feedback or information. :bow: The solution to the Poisson equation -\Delta u(x)=\frac{q}{\pi...
17. ### B Poisson distribution having variation coefficient = .5?

Variation coefficient is calculated by And the very definition of poisson distribution is that $$\mu = \sigma$$ So how would any other value but 1 be a possible?
18. ### Poisson Ratio -- Finding a corresponding analytical solution for the strain

Hi, I ran into problems using the poisson ratio. For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge. Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir. The material parameters are E = 100, and v...
19. ### A Average of the power spectrum of Poisson noise

I am learning about noise that follows a Poisson distribution. When I do a Fourier transform of the data with only Poisson noise to get the power spectrum, what is the average value of the power spectrum?
20. ### A Why the Poisson noise level is set to 2 after applying Leahy norm

I am studying about power spectrum analysis in high energy astrophysics. I cannot understand why the Poisson noise level is set to 2 after applying Leahy normalization. $$P_{j}=2 /_{N \mathrm{ph}}\left|a_{j}\right|^{2}$$ The above is the equation for leahy norm, Can I expand the equation from...