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In statistics, the probability distributions of discrete variables can be expressed in terms of [[probability mass function]]s.<ref name="Springer Texts in Statistics" />
In [[discrete time]] dynamics, the variable ''time'' is treated as discrete, and the equation of evolution of some variable over time is called a [[difference equation]].<ref>{{cite book |last1=Thyagarajan |first1=K.S. |title=Introduction to Digital Signal Processing Using MATLAB with Application to Digital Communications |date=2019 |publisher=Springer Publishing Company |isbn=978-3319760285 |pages=21–63 |edition=1}}</ref> For certain discrete-time dynamical systems, the system response can be
In [[econometrics]] and more generally in [[regression analysis]], sometimes some of the variables being [[empirical]]ly related to each other are 0-1 variables, being permitted to take on only those two values.<ref>{{cite journal |last1=Miller |first1=Jerry L.L. |last2=Erickson |first2=Maynard L. |title=On Dummy Variable Regression Analysis |journal=Sociological Methods & Research |date=May 1974 |volume=2 |issue=4 |pages=395–519 |doi=10.1177/004912417400200402}}</ref> The purpose of the discrete values of 0 and 1 is to use the dummy variable as a ‘switch’ that can ‘turn on’ and ‘turn off’ by assigning the two values to different parameters in an equation. A variable of this type is called a [[dummy variable (statistics)|dummy variable]]. If the [[dependent variable]] is a dummy variable, then [[logistic regression]] or [[probit regression]] is commonly employed. In the case of regression analysis, a dummy variable can be used to represent subgroups of the sample in a study (e.g. the value 0 corresponding to a constituent of the control group).<ref>{{cite book |last1=Hardy |first1=Melissa A. |title=Regression with Dummy Variables (Quantitative Applications in the Social Sciences) |date=February 25, 1993 |publisher=Sage Publications, Inc. |___location=Newbury Park |isbn=0803951280 |page=v |edition=1st}}</ref>
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