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In page Degenerate distribution:

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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. For example, in the 2-variable case suppose that Y = aX + b for scalar random variables X and Y and scalar constants a ≠ 0 and b; here knowing the value of one of X or Y gives exact knowledge of the value of the other. All the possible points (x, y) fall on the one-dimensional line y = ax + b.[citation needed]