Integral Identities for Random Variables.

Abstract

Using a general method for deriving identities for random variables, the author finds a number of new results involving characteristic functions and generating functions. The method is simply to promote a parameter in an integral relation to the status of a random variable and then take expected values of both sides of the equation. Results include formulas for calculating the characteristic functions for sq x, square root of x, 1/x, sq x + x, sq R = sq x + sq y, etc. in terms of integral transforms of the characteristic functions for x and (x,y), etc. Generalizations to higher dimensions can be obtained using the same method. Expressions for inverse/ fractional moments, E(n ), etc. are also presented, demonstrating the method.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1986
Accession Number
ADA174362

Entities

People

  • Edward B. Rockower

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Bessel Functions
  • Difference Equations
  • Equations
  • Identities
  • Infinite Series
  • Integral Transforms
  • Integrals
  • Normal Distribution
  • Numbers
  • Operations Research
  • Power Series
  • Probability
  • Probability Distributions
  • Random Variables
  • Standards
  • Stochastic Processes
  • Technical Information Centers

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Systems Analysis and Design