# What is the difference between a normal distribution, binomial distribution, and a Poisson distribution?

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Feb 24, 2016

While in Binomial and Poisson distributions have discreet random variables, the Normal distribution is a continuous random variable. Poisson and Normal distribution are special cases of Binomial distribution.

#### Explanation:

While in Binomial and Poisson distributions have discreet random variables, the Normal distribution is a continuous random variable.

Binomial distribution (with parameters $n$ and $p$) is the discrete probability distribution of the number of successes in a sequence of $n$ independent experiments, each of which yields success with probability $p$.

Poisson distribution can be derived from the binomial distribution. It is nothing more than the limiting case of the Binomial where $n$ is large and $p$ is small (say close to zero) but $n p$ is finite.

Normal distribution is a continuous distribution, completely described by two parameters $\mu$ and $\sigma$, where $\mu$ represents the population mean or center of the distribution and $\sigma$ the population standard deviation. It too can be derived from Binomial Distribution, if $n$ is too large but $p$ is not small enough.

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