Category:Degenerate Distribution

This category contains results about the degenerate distribution.

Let $X$ be a discrete random variable on a probability space.

Then $X$ has a degenerate distribution with parameter $r$ if and only if:

$\Omega_X = \set r$

$\map \Pr {X = k} = \begin {cases} 1 & : k = r \\ 0 & : k \ne r \end {cases}$

That is, there is only value that $X$ can take, namely $r$, which it takes with certainty.