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Rayleigh PDF

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Show that the average (mean), mean-square, and median values of the Rayleigh PDF for amplitude are given by the equations listed in the attachment.

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Solution Summary

The solution explains its steps as it performs the calculations to show that the average of the Rayleigh PDF amplitude is given by the listed equations.

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p(A) = [A/A0^2]exp[-{A^2/2*A0^2}], A>= 0

1. Average (Mean)

Integral (A=0 to infinity)[A*p(A) dA]
= (1/A0^2)*Integral (A=0 to infinity)[A^2exp{-(A^2/2*A0^2)} dA

Now from standard Integral table we get,

Integral (x=0 to infinity)[x^2exp{-(a*x^2)} dx = (1/4a)sqrt(pi/a)

Here a = ...

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