Some Properties of Dimensional Probability Vectors
- Probability vectors of dimension are contained within an dimensional unit hyperplane.
- The mean of a probability vector is .
- The shortest probability vector has the value as each component of the vector, and has a length of .
- The longest probability vector has the value 1 in a single component and 0 in all others, and has a length of 1.
- The shortest vector corresponds to maximum uncertainty, the longest to maximum certainty.
- No two probability vectors in the dimensional unit hypersphere are collinear unless they are identical.
- The length of a probability vector is equal to ; where is the variance of the elements of the probability vector.
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