If X and Y are i.i.d Poisson variables with lambda1 and lambda2 then,
P (X = x | X + Y = n) ~ Bin(n, p) where p = lambda1 / lambda1 + lambda2
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The Poisson distribution is a limiting case of the binomial distribution when the number of trials is very large and the probability of success is very small. The Poisson distribution is used to model the number of occurrences of rare events in a fixed interval of time or space, while the binomial distribution is used to model the number of successful outcomes in a fixed number of trials.
In a symmetric binomial distribution, the probabilities of success and failure are equal, resulting in a symmetric shape of the distribution. In a skewed binomial distribution, the probabilities of success and failure are not equal, leading to an asymmetric shape where the distribution is stretched towards one side.
Poisson's equation relates the distribution of electric charge to the resulting electric field in a given region of space. It is a fundamental equation in electrostatics that helps to determine the electric potential and field in various situations, such as around point charges or within conductors. Mathematically, it represents the balance between the charge distribution and the electric field that it produces.
The assumptions of the binomial distribution are that there are a fixed number of independent trials, each trial has two possible outcomes (success or failure), the probability of success is constant across all trials, and the outcomes of each trial are independent of each other.
In binomial nomenclature, the genus represents the first part of the scientific name and groups together species that are closely related and share certain characteristics. It is a level of classification above species and below family.
the french call a goldfish "un poisson rouge" - a red fish. desription could maybe be: un poisson rouge est un animal domestique qui habite dans un petit aquarium dans la maison