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Incoming links: Order symmetry of independent random variables
Past exam of the mathematics course of the University of Cambridge 2007 ia Paper 2 9F Solution Created 2026-09-24 Updated 2026-09-24
Past exam of the mathematics course of the University of Cambridge 2016 ia Paper 2 3F Solution Created 2026-09-24 Updated 2026-10-06
The independent and identically distributed random variables have a continuous probability distribution, so any tie has probability zero. Their joint probability density is unchanged by a permutation of their indices: this is order symmetry of independent random variables. The strict orderings are disjoint and exhaust the sample space apart from the zero-probability ties. Each ordering therefore has the same probability, and their probabilities sum to one.
The probability is