proposition 11.24 The algebra of the discrete case transfers

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:634 · p. 378

Rests on

depends_on definition 11.23 Expectation, moments and quantiles in the continuous case ¶
- depends_on definition 11.20 Density ¶
  - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶
- 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 7.2 Absolute value ¶ ↺
  - depends_on definition 11.3 Discrete random variable ¶
    - depends_on definition 11.1 Discrete probability space ¶
      - depends_on definition 7.45 Series ¶ ↺
depends_on proposition 11.5 Transfer, linearity, monotonicity ¶
- depends_on definition 11.4 Expectation ¶ ↺
- 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 ¶
proves proof ch:09-probability-statistics@proof-10 ¶

Supports

depends_on example 11.30 Exponential lifetimes ¶
depends_on proposition 11.26 Product rule ¶

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`	→	Expectation, moments and quantiles in the continuous case	declared	parts/02-mathematical-methods/09-probability-statistics.tex:641
`depends_on`	→	Transfer, linearity, monotonicity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:641
`depends_on`	←	Exponential lifetimes	declared	parts/02-mathematical-methods/09-probability-statistics.tex:793
`depends_on`	←	Product rule	declared	parts/02-mathematical-methods/09-probability-statistics.tex:681
`proves`	←	ch:09-probability-statistics@proof-10	declared	parts/02-mathematical-methods/09-probability-statistics.tex:644