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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.

    © BrainMass Inc. brainmass.com May 24, 2023, 1:32 pm ad1c9bdddf


    Solution Preview

    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 = ...

    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.