In order to model a discrete random variable that assumes a value $x_i$ we construct a discrete distribution with sums of [Dirac delta function](Dirac%20delta%20function.md) where the distribution is $\rho(x)=\sum_{i=1}^n P_i\,\delta(x-x_i)$ where $P_i$ is the probability associated with a result $x_i$ thus, $\sum_i P_i = 1.$ # Trivial discrete probability distribution A _trivial_ discrete probability distribution is a distribution containing only one value, $x_1$ which we know with certainty (so that $P_1=1$) and the distribution is simply $\rho(x)=\delta(x-x_1).$ #MathematicalFoundations/StatisticsAndProbability/ProbabilityDistributions #MathematicalFoundations/StatisticsAndProbability/ProbabilityDistributions/DiscreteProbabilityDistributions