iid

iid or i.i.d. is an acronym that stands for independent and identically distributed, with reference to two or more random variables. Two or more iid variables are independent of each other and all follow the same Probability distribution. They are a particularly simple case of a set of random variables, as the probability of a specific set of outcomes occurring is just the product of the probabilities of each outcome happening independently:

P(x1,…,xN)=∏i=1Np(xi)P(x_{1},\ldots,x_{N})=\prod_{i=1}^{N} p(x_{i})

where pp is the Probability mass function or Probability density function of the variables.