Is there an expression for the integral of an arbitrary CDF?

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    Cdf Integral
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The discussion centers on finding an expression for the integral of an arbitrary cumulative distribution function (CDF), denoted as ∫ F(x)dx. Participants suggest that if F represents a continuous distribution, integration by parts may be a viable method to derive an equivalent expression. The conversation emphasizes the importance of understanding the properties of distribution functions in the context of integration.

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  • Understanding of cumulative distribution functions (CDFs)
  • Knowledge of integration techniques, specifically integration by parts
  • Familiarity with continuous probability distributions
  • Basic calculus concepts
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  • Research the application of integration by parts in probability theory
  • Explore the properties of continuous distribution functions
  • Study the relationship between CDFs and probability density functions (PDFs)
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shoeburg
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Let F be any distribution function. With either the indefinite integral, or taking limits at plus and minus infinity, is there an equivalent expression to ∫ F(x)dx ? Can we derive one?

Thanks.
 
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If F yields a continuous distribution, you might think about integration by parts.
 

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