proposition 11.27 Probability integral transform

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 11.22 Properties of the distribution function ¶
  • depends_on definition 11.21 Distribution function ¶
    • depends_on definition 11.20 Density ¶ ↺
  • depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
    • depends_on definition 7.26 Derivative of a function at a point ¶
      • depends_on definition 7.16 Limit ¶
        • depends_on definition 7.2 Absolute value ¶ ↺
        • depends_on definition 7.9 Real function ¶
      • depends_on definition 7.9 Real function ¶ ↺
    • depends_on theorem 7.40 Continuous functions are integrable ¶
      • depends_on definition 7.39 Darboux sums and the definite integral ¶ ↺
      • depends_on theorem 7.24 Extreme value theorem ¶
        • depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
        • depends_on proposition 7.22 Sequential characterization ¶
        • depends_on theorem 7.7 Bolzano–Weierstrass ¶
        • proves proof ch:05-real-analysis@proof-9 ¶
      • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
        • depends_on proposition 7.22 Sequential characterization ¶ ↺
        • depends_on theorem 7.7 Bolzano–Weierstrass ¶ ↺
        • proves proof ch:05-real-analysis@proof-10 ¶
      • proves proof ch:05-real-analysis@proof-23 ¶
    • depends_on theorem 7.24 Extreme value theorem ¶ ↺
    • proves proof ch:05-real-analysis@proof-24 ¶
  • proves proof ch:09-probability-statistics@proof-9 ¶
• proves proof ch:09-probability-statistics@proof-12 ¶

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