OurBigBook About$ Donate
 Sign in Sign up

Past exam of the mathematics course of the University of Cambridge / 2016 / ia / Paper 2 / 3F / Solution

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2016 ia Paper 2 3F
Created 2026-09-24 Updated 2026-10-06  0 By others on same topic  0 Discussions Create my own version
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 n! 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
P(X1​>X2​>⋯>Xn​)=n!1​.​
(1)

 Ancestors (10)

  1. 3F
  2. Paper 2
  3. ia
  4. 2016
  5. Past exam of the mathematics course of the University of Cambridge
  6. Mathematics course of the University of Cambridge
  7. Course of the University of Cambridge
  8. University of Cambridge
  9. List of universities
  10.  Home

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook