proposition 11.12 Bilinearity

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:328 · p. 374

Rests on

depends_on definition 11.11 Covariance and correlation ¶
- 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 11.3 Discrete random variable ¶
    - 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 ¶ ↺
depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
proves proof ch:09-probability-statistics@proof-5 ¶

Supports

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 example 11.19 A counting measurement ¶ ↺
  - depends_on example 11.31 A length measurement ¶
depends_on proposition 11.17 Sampling identities ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Covariance and correlation	declared	parts/02-mathematical-methods/09-probability-statistics.tex:341
`depends_on`	→	Transfer, linearity, monotonicity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:341
`depends_on`	←	Three standard discrete distributions	declared	parts/02-mathematical-methods/09-probability-statistics.tex:523
`depends_on`	←	Independence implies zero covariance; the converse fails	declared	parts/02-mathematical-methods/09-probability-statistics.tex:375
`depends_on`	←	Sampling identities	declared	parts/02-mathematical-methods/09-probability-statistics.tex:466
`proves`	←	ch:09-probability-statistics@proof-5	declared	parts/02-mathematical-methods/09-probability-statistics.tex:344