MATLAB: How to integrate a bivariate function over 1 dimension

bivariate pdf integral

I have a bivariate normal pdf that I wold like to integrate over only 1 dimension. Does anyone have advice on how to do this? Thank you!

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syms x y rho ux uy real
syms sx sx positive
syms pi
assume(-1 <= rho & rho <= 1)
f = 1/(2*pi*sx*sy*sqrt(1-rho^2)) * exp(-1/(2*(1-rho^2))*((x-ux)^2/sx^2 + (y-uy)^2/sy^2 - 2*rho*(x-ux)*(y-uy)/(sx*sy)))
pretty(f)
result = int(f,x,-inf,inf)

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MATLAB: Symbolic integration for chi-square distribution

Possibly you will have to go back to the definition of chi2pdf that is on the documentation page, http://www.mathworks.com/help/toolbox/stats/chi2pdf.html as chi2pdf routine is a numeric routine rather than a symbolic routine.

MATLAB: Conditioning bivariate gaussian distribution

There a few issues with your code.

First INTEGRAL is integration of a scalar function, you cannot integrate a vector function. So in 1D you need to loop in the parameters (x) or (y).

Second parameters ans variable are no longer have the same length, you can not do vercat them.

Here is a modified code

mu_x = 0;
c =  [0.5 0.8; 0.8 2.0];
% this block is irrelevant!!!
% x1 = -4:0.2:4;
% x2 = -4:0.2:4;
% [X1,X2] = meshgrid(x1,x2);
% X = X1(:)';
% Y = X2(:)';
fun = @(X, Y) gfun(X,Y,mu_x,c); % nested defined bellow 
px = @(X) arrayfun(@(x) integral(@(y)fun(x,y),-inf,inf,'ArrayValued',true), X);
py = @(Y) arrayfun(@(y) integral(@(x)fun(x,y),-inf,inf,'ArrayValued',true), Y);
Pxy = [px([-3:0.2:3]); py([-3:0.2:3])]
close all
plot(Pxy')
%%
function f = gfun(X,Y,mu,c)
[X,Y] = ndgrid(X(:)',Y(:)'); % expanding the scalar to match the vector, regardless which is which
XY = [X; Y];
f = 1/(2*pi*(det(c))^(0.5))* exp(-(0.5)*sum((XY-mu).*(c\(XY-mu))));
end

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MATLAB: Symbolic integration for chi-square distribution

MATLAB: Conditioning bivariate gaussian distribution

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