Examples include a two-headed coin and rolling a die whose sides all show the same number.

[2][better source needed] The probability mass function equals 1 at this point and 0 elsewhere.

[citation needed] The degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta function at k0, with infinite height there but area equal to 1.

[citation needed] In probability theory, a constant random variable is a discrete random variable that takes a constant value, regardless of any 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.

[citation needed] Degeneracy of a multivariate distribution in n random variables arises when the support lies in a space of dimension less than n.[1] This occurs when at least one of the variables is a deterministic function of the others.

[citation needed] In general when one or more of n random variables are exactly linearly determined by the others, if the covariance matrix exists its rank is less than n[1][verification needed] and its determinant is 0, so it is positive semi-definite but not positive definite, and the joint probability distribution is degenerate.

For example, when scalar X is symmetrically distributed about 0 and Y is exactly given by Y = X2, all possible points (x, y) fall on the parabola y = x2, which is a one-dimensional subset of the two-dimensional space.