proposition 11.7 Variance identity

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:207 · p. 373

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 ¶ ↺
proves proof ch:09-probability-statistics@proof-3 ¶

Supports

depends_on proposition 11.10 What the mean and the median minimise ¶
- depends_on example 11.30 Exponential lifetimes ¶

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`	→	Moments, variance, standard deviation	declared	parts/02-mathematical-methods/09-probability-statistics.tex:215
`depends_on`	→	Transfer, linearity, monotonicity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:215
`depends_on`	←	What the mean and the median minimise	declared	parts/02-mathematical-methods/09-probability-statistics.tex:276
`proves`	←	ch:09-probability-statistics@proof-3	declared	parts/02-mathematical-methods/09-probability-statistics.tex:218