calcuating expected value from a joint distribution

Hi Everyone,

I am really struggling with this problem so i really hope someone can help me out.

My problem is as follows: I have random variables I will call xand y, and for which I have a joint pdf f(x,y). My question is: how can I compute the expected value of x/y, that is:

E(x/y)=DoubleIntegral(x/y*f(x,y)dx dy)???

i tried to use dblquad to do the integral using mvnpdf to generate a normal joint distribution of X and Y as a trial but i get errors and i cant figure out a way to go...any help wld be greatly appreciated, Thanks!

Answer 1

[Tom Lane]

You don't say what errors you get.

You could get problems if you are in a region where y is near zero. Away from that region, here's an example where I compute the mean of a sample from the distribution, then verify it is close to the value I get by integrating over a finite but large region:

>> mu = [10 10];
>> sigma = [1 1;1 2];
>> xy = mvnrnd(mu,sigma,1000);
>> mean(xy(:,1)./xy(:,2))
ans =
    1.0103
>> dblquad(@(x,y)(x(:)./y).*mvnpdf([x(:) repmat(y,numel(x),1)],mu,sigma),1,20,1,20)
ans =
    1.0107