The Darth Vader rule

Pat Muldowney; Krzysztof Ostaszewski; Wojciech Wojdowski

doi:10.2478/v10127-012-0025-9

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The Darth Vader rule

Tatra Mountains Mathematical Publications

Volume 52 (2012): Issue 1 (August 2012)

By: Pat Muldowney, Krzysztof Ostaszewski and Wojciech Wojdowski

Open Access

|Nov 2012

Abstract

Using Henstock’s generalized Riemann integral, we show that, for any almost surely non-negative random variable X with probability density function fX and survival function s_X(x) := ∫∞ _x f_X(t) dt, the expected value of X is given by E(Xz) = ∫^∞₀ f_X(x) dx.

References

[1] FELLER, W.: An Introduction to Probability Theory and its Applications. Vol. 2. John Wiley & Sons, Inc. New York, 1966.
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[2] HENSTOCK, R.: Lectures in the Theory of Integration. World Scientific, Singapore, 1988.10.1142/0510
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[3] HEWITT, E.: Integration by parts for Stieltjes integrals, Amer.Math.Monthly 67 (1960), 419-423, http://www.jstor.org/stable/2309287
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[4] KURZWEIL, J.: Generalized ordinary differential equations and continuous dependenceon a parameter, Czechoslovak Math. J. 82 (1957), 418-446.10.21136/CMJ.1957.100258
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Articles in this issue

DOI: https://doi.org/10.2478/v10127-012-0025-9 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 53 - 63

Published on: Nov 19, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

expected value,

Henstock integral,

integration by parts.

Related subjects:

Mathematics,

General mathematics

© 2012 Pat Muldowney, Krzysztof Ostaszewski, Wojciech Wojdowski, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 52 (2012): Issue 1 (August 2012)