definition 11.11 Covariance and correlation

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:310 · p. 374

ground object -- no derivation owed

Rests on

depends_on definition 11.6 Moments, variance, standard deviation ¶
- depends_on proposition 11.5 Transfer, linearity, monotonicity ¶
  - depends_on definition 11.4 Expectation ¶
    - depends_on definition 7.45 Series ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.4 Convergence ¶
    - depends_on definition 11.3 Discrete random variable ¶
      - depends_on definition 11.1 Discrete probability space ¶
  - depends_on proposition 11.2 Elementary rules ¶
    - depends_on definition 11.1 Discrete probability space ¶ ↺
    - proves proof ch:09-probability-statistics@proof-1 ¶
  - proves proof ch:09-probability-statistics@proof-2 ¶
depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺

Supports

depends_on corollary 11.15 Bounds on the correlation coefficient ¶
depends_on definition 11.16 Sample mean, variance and correlation ¶
- depends_on example 11.19 A counting measurement ¶
- depends_on example 11.31 A length measurement ¶
- depends_on proposition 11.17 Sampling identities ¶
  - depends_on example 11.19 A counting measurement ¶ ↺
  - depends_on example 11.31 A length measurement ¶ ↺
depends_on lemma 11.63 Cauchy–Schwarz for random variables ¶
- depends_on corollary 11.15 Bounds on the correlation coefficient ¶ ↺
- depends_on corollary 11.65 When the bound is attained ¶
- depends_on lemma A.199 The standardised third moment is at least one ¶
  - depends_on lemma A.200 Transform estimate ¶
- depends_on theorem 11.64 Cramér–Rao inequality ¶
  - depends_on corollary 11.65 When the bound is attained ¶ ↺
  - depends_on example 11.62 Information in a counting experiment ¶
depends_on proposition 11.12 Bilinearity ¶
- depends_on example 11.18 Three standard discrete distributions ¶
  - depends_on example 11.19 A counting measurement ¶ ↺
- depends_on proposition 11.14 Independence implies zero covariance; the converse fails ¶
  - depends_on example 11.18 Three standard discrete distributions ¶ ↺
  - depends_on proposition 11.17 Sampling identities ¶ ↺
- depends_on proposition 11.17 Sampling identities ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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partly declared
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Edges

type	direction	node	provenance	where
`depends_on`	→	Moments, variance, standard deviation	declared	parts/02-mathematical-methods/09-probability-statistics.tex:325
`depends_on`	→	Transfer, linearity, monotonicity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:325
`depends_on`	←	Bounds on the correlation coefficient	declared	parts/02-mathematical-methods/09-probability-statistics.tex:407
`depends_on`	←	Sample mean, variance and correlation	declared	parts/02-mathematical-methods/09-probability-statistics.tex:453
`depends_on`	←	Cauchy–Schwarz for random variables	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1806
`depends_on`	←	Bilinearity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:341