Math 2.0

Probability theory and stochastic processes Definition

Discrete uniform distribution

Builds on Probability mass functionClassical definition of probabilityFinite set

Definition

Let SS be a nonempty finite set with nn elements. The discrete uniform distribution on SS is the distribution with the probability mass function p(s)=1nfor s∈S.p(s) = \frac{1}{n} \quad \text{for } s \in S. A random variable XX is uniform on SS if P(X=s)=1/nP(X = s) = 1/n for each s∈Ss \in S.

Remarks

Then P(X∈A)=∣A∣/nP(X \in A) = |A| / n for each A⊆SA \subseteq S. This is the classical definition of probability. For S={a,a+1,…,b}S = \{a, a + 1, \dots, b\} with integers a≤ba \le b and n=b−a+1n = b - a + 1, the mean is (a+b)/2(a + b)/2 and the variance is (n2−1)/12(n^2 - 1)/12. The result of a fair die is uniform on {1,…,6}\{1, \dots, 6\}, with mean 7/27/2.

Reading path

To understand this page from the ground up, read these 49 pages in order. The foundations come first.

  1. Construction of the reals from Cauchy sequences concept
  2. Element definition
  3. Integers object
  4. Ordered field definition
  5. Proposition concept
  6. Random experiment concept
  7. Rational numbers object
  8. Real numbers object
  9. Set definition
  10. Ring of integers statement
  11. Disjunction definition
  12. Implication definition
  13. Predicate definition
  14. Ordered pair definition
  15. Union definition
  16. Sample space definition
  17. The rationals form a field statement
  18. Existential quantifier definition
  19. Universal quantifier definition
  20. Cartesian product definition
  21. Subset definition
  22. The rationals form an ordered field statement
  23. Uniqueness quantifier definition
  24. Binary relation definition
  25. Universal set definition
  26. Order on the reals definition
  27. Power set definition
  28. Complement definition
  29. Function definition
  30. Interval definition
  31. Codomain definition
  32. Injective function definition
  33. Preimage of a set definition
  34. Sigma-algebra definition
  35. Surjective function definition
  36. Countable set definition
  37. Event definition
  38. Borel sigma-algebra definition
  39. Bijective function definition
  40. Probability axioms concept
  41. Equinumerous sets definition
  42. Probability measure definition
  43. Finite set definition
  44. Probability space definition
  45. Classical definition of probability definition
  46. Random variable definition
  47. Discrete random variable definition
  48. Probability mass function definition
  49. Discrete uniform distribution definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Discrete_uniform_distribution, lead section
About this page
Tag0KYP951QWH
URIm2://0KYP951QWH
Kinddefinition
WritingW1 stated
MSC60E05
DefinesDiscrete uniform distribution
UsesProbability mass function, Classical definition of probability, Finite set

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.