Mohammed Abaza

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6 years, 78 days

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These are questions asked by Mohammed Abaza

Please help me to solve this integration

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity);

 

 

 

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity)

Please I want to know how to solve this integration.

 

int(exp(-(ln(y)-2*sigma^2)^2/(8*sigma^2))/(y*sqrt(8*Pi*sigma^2))*exp(-(ln(y+z)-2*sigma^2)^2/(8*sigma^2))/((y+z)*sqrt(8*Pi*sigma^2)), y = 0 .. infinity)

Please could you please help me finding closed expression for the following double integral

 

restart;

with(LinearAlgebra);

rho := .25; sigma := .1; SNR := 25;                                                                    

 a := (32*12)*Pi*sqrt(1-rho^2...

Please help me in this integration. It does not work.  

 

restart;with(LinearAlgebra); with(linalg);
Q := x->0.5*erfc(x/sqrt(2));
rho:=0.25;sigma := 0.3;

m1 := sigma*sigma*Matrix(3, 3, [1, rho, rho^2, rho, 1, rho, rho^2, rho, 1]);

SNR := 15; mu := evalf(10^(.1*SNR));
 
 a := Matrix(1, 3, [(ln(y/mu)+4*sigma^2)^2, (ln(y1/mu)+4*sigma^2)^2,
 (ln(y2/mu)+4*sigma^2)^2]);
Please Help me:
First to solve this integration note that it is working if sigma=0.1.
Secondly I want to increase the accuracy of the result of sigma=0.1 as
there is slight difference between this numerical integration and montecarlo simulation 
using MATLAB.
 
restart;Q := x->0.5*erfc(x/sqrt(2));

sigma := 0.3;

SNR := [seq(1 .. 25, 1)]; for i in SNR do mu := evalf(10^(.1*i));
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