Question

define poisson distribution. state its mean and variance

Answer 1

A Poisson random variable is the number of successes that result from a Poisson experiment. The probability distribution of a Poisson random variable is called a Poisson distribution.
Poisson Formula. Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is μ. Then, the Poisson probability is:

P(x; μ) = (e-μ) (μx) / x!

where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.
The Poisson distribution has the following properties:

The mean of the distribution is equal to μ .
The variance is also equal to μ .

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