A standard normal deviate is a normally distributed deviate. It is a realization of a standard normal random variable, defined as a random variable with expected value 0 and variance 1. Where collections of such random variables are used, there is often an associated (possibly unstated) assumption that members of such collections are statistically independent. Standard normal variables play a major role in theoretical statistics in the description of many types of models, particularly in regression analysis, the analysis of variance and time series analysis. When the term "deviate" is used, rather than "variable", there is a connotation that the value concerned is treated as the no-longer-random outcome of a standard normal random variable. The terminology here is the same as that for random variable and random variate. Standard normal deviates arise in practical statistics in two ways.