Uniform (continuous)

All values in the range are equally likely. Mean=a/2, variance=a²/12. Here we use f(x) to denote the probability distribution associated with continuous valued variables x, also described as a probability density function

Binomial (discrete)

The terms of the Binomial give the probability of x successes out of n trials, for example 3 heads in 10 tosses of a coin, where p=probability of success and q=1‑p=probability of failure. Mean, m=np, variance=npq. Here we use p(x) to denote the probability distribution associated with discrete valued variables x

; x=1,2,…n

Poisson (discrete)

An approximation to the Binomial when p is very small and n is large (>100), but the mean m=np is fixed and finite (usually not large). Mean=variance=m

; x=1,2,…n

Normal (continuous)

The distribution of a measurement, x, that is subject to a large number of independent, random, additive errors. The Normal distribution may also be derived as an approximation to the Binomial when p is not small (e.g. p≈1/2) and n is large. If μ=mean and σ=standard deviation, we write N(μ,σ) as the Normal distribution with these parameters. The Normal- or z-transform z=(x‑μ)/σ changes (normalizes) the distribution so that it has a zero mean and unit variance, N(0,1). The distribution of n mean values of independent random variables drawn from any underlying distribution is also Normal (Central Limit Theorem)