Editing Degenerate distribution (section)

==Constant random variable==
A '''constant random variable''' is a [[discrete random variable]] that takes a [[Constant function|constant]] value, regardless of any [[event (probability theory)|event]] that occurs.  This is technically different from an '''[[almost surely]] constant random variable''', which may take other values, but only on events with probability zero:
Let {{math|''X'': Ω → ℝ}} be a real-valued random variable defined on a probability space {{math|(Ω, ℙ)}}.  Then {{mvar|X}} is an ''almost surely constant random variable'' if there exists <math>a \in \mathbb{R}</math> such that
<math display="block">\mathbb{P}(X = a) = 1,</math>
and is furthermore a ''constant random variable'' if
<math display="block">X(\omega) = a, \quad \forall\omega \in \Omega.</math>
A constant random variable is almost surely constant, but the converse is not true, since if {{mvar|X}} is almost surely constant then there may still exist {{math|γ ∈ Ω}} such that {{math|''X''(γ) ≠ a}}.

For practical purposes, the distinction between {{mvar|X}} being constant or almost surely constant is unimportant, since these two situation correspond to the same degenerate distribution: the Dirac measure.