<abstract xmlns="http://www.w3.org/1999/xhtml"> Using Henstock’s generalized Riemann integral, we show that, for any almost surely non-negative random variable <italic>X </italic>with probability density function <italic>fX </italic>and survival function <italic>s</italic>X(<italic>x</italic>) := ∫∞ <italic>x f</italic>X(<italic>t</italic>) <italic>dt</italic>, the expected value of <italic>X </italic>is given by <bold>E</bold>(<italic>Xz</italic>) = ∫∞0 f<italic>X</italic>(<italic>x</italic>) <italic>dx</italic>.</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 sX(x) := ∫∞ x fX(t) dt, the expected value of X  is given by E(Xz) =  ∫∞0 fX(x) dx.

The Darth Vader rule

University of Ulster Lisselty Dunmore East County Waterford IRELAND

Department of Mathematics Stevenson Hall 313G Illinois State University Normal, IL 61790–4520 U.S.A.

Institute of Mathematics Technical University of Łódź ul. Wólczańska 215 93-005 Łódź POLAND

Tatra Mountains Mathematical Publications

{"article-title":"The Darth Vader rule"}

Using Henstock’s generalized Riemann integral, we show that, for any almost surely non-negative random variable X with probability density function fX and...

The Darth Vader rule

Published Online: Nov 19, 2012

Page range: 53 - 63

DOI: https://doi.org/10.2478/v10127-012-0025-9

Keywords
expected value, Henstock integral, integration by parts.

This content is open access.

The Darth Vader rule

Published Online: Nov 19, 2012

Page range: 53 - 63

DOI: https://doi.org/10.2478/v10127-012-0025-9

Keywordsexpected value, Henstock integral, integration by parts.

This content is open access.

Keywords
expected value, Henstock integral, integration by parts.