lemma 11.50 Markov and Chebyshev inequalities

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:1401 · p. 387

Rests on

depends_on corollary 11.51 Weak law of large numbers ¶
- depends_on theorem A.205 Weak law under integrability alone ¶
  - depends_on lemma A.208 The three averages ¶
    - depends_on corollary A.210 Uniform quadratic approximation on the $n^{-1/2}$ scale ¶
      - depends_on lemma A.213 The three minima ¶
    - depends_on lemma A.211 Root-$n$ localisation ¶
      - depends_on lemma A.213 The three minima ¶ ↺
- depends_on theorem 11.67 Asymptotics of the MLE ¶
  - depends_on proposition 11.72 Nuisance parameters cost information ¶
  - depends_on theorem 11.88 Wilks ¶
    - depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶
      - depends_on example 11.107 Degrading a local five sigma ¶
      - depends_on proposition 11.93 $Z=\sqrt{q}$ ¶
      - depends_on remark 11.90 Failure I: a parameter on the boundary ¶
depends_on theorem 11.101 Davies' bound ¶
- depends_on corollary 11.105 Trials factor at high significance ¶
- depends_on example 11.107 Degrading a local five sigma ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Moments, variance, standard deviation	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1408
`depends_on`	→	Transfer, linearity, monotonicity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1408
`depends_on`	←	Weak law of large numbers	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1424
`depends_on`	←	Davies' bound	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3101
`proves`	←	ch:09-probability-statistics@proof-18	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1411