Register to reply

Deriving the second raw moment of the rice PDF

by kstephe6
Tags: deriving, moment, rice
Share this thread:
Mar5-12, 09:40 AM
P: 3
(the following is Mathematica code)

For the rice pdf...

P(x)=(x/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)]

...the Second raw moment is given by doing the integral...

Integrate[(x^3/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)], {x, 0, Infinity}]

While the answer is known to be...

2 σ^2 + ν^2

...I have no idea how to arrive at this answer by hand (ie without using Mathematica). I am currently doing a little research for grins and giggles on a very closely related integral, and knowing how to solve the one above would be of great use to me. Any help in this endeavor... Even suggestions as to where I might find the derivation... would be greatly appreciated.
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
Mar5-12, 10:43 AM
P: 3
FYI, this is exactly the same problem as finding <x^2> (the average of the square) for P(x)
Mar7-12, 05:39 AM
P: 3
Never mind... I figured it out. The answer is very lengthy, so If anyone is curious just let me know. Otherwise, I'm not taking the time to post 3 pages of recursive formulas and integration by parts.

Register to reply

Related Discussions
Deriving the first moment of area of semicircle Engineering, Comp Sci, & Technology Homework 3
Deriving moment of Inertia Introductory Physics Homework 2
Help Deriving formula for moment of inertia lab Introductory Physics Homework 1
Deriving the moment of inertia for a sphere Calculus & Beyond Homework 4
Deriving Moment of Inertia Introductory Physics Homework 2