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 methodPrepared for: Commander, Space and Naval Warfare Systems Command
Washington, D.C.http://archive.org/details/integralidentiti00rockN0003986WRDJ850NAApproved for public release; distribution is unlimited
