example 11.30 Exponential lifetimes

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:773 · p. 379

example -- no derivation owed by its kind

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 11.10 What the mean and the median minimise ¶
- depends_on definition 11.8 Quantiles and median ¶
  - depends_on definition 11.3 Discrete random variable ¶ ↺
- depends_on proposition 11.7 Variance identity ¶
  - 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 proposition 11.2 Elementary rules ¶
      - proves proof ch:09-probability-statistics@proof-2 ¶
  - depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
  - proves proof ch:09-probability-statistics@proof-3 ¶
- proves proof ch:09-probability-statistics@proof-4 ¶
depends_on proposition 11.24 The algebra of the discrete case transfers ¶
- depends_on definition 11.23 Expectation, moments and quantiles in the continuous case ¶ ↺
- depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
- proves proof ch:09-probability-statistics@proof-10 ¶

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type	direction	node	provenance	where
`depends_on`	→	Expectation, moments and quantiles in the continuous case	declared	parts/02-mathematical-methods/09-probability-statistics.tex:793
`depends_on`	→	What the mean and the median minimise	declared	parts/02-mathematical-methods/09-probability-statistics.tex:793
`depends_on`	→	The algebra of the discrete case transfers	declared	parts/02-mathematical-methods/09-probability-statistics.tex:793