Question

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

Answer 1

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 `np` 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.