Say I have a non-linear equation, take y = a^2 + b^2 as an example.
If I know the variance on a and b, what is the variance on y?
I know that generally, sigma_y^2 = (dy/da)^2*sigma_a^2 + (dy/db)^2*sigma_b^2. But, what I don't understand is with this nonlinear equation, my partial derivatives are still a function of a and b respectively. So, if I have:
sigma_y^2 = 4a^2*sigma_a^2 + 4b^2*sigma_b^2 (assuming covariance is 0),
what do I use for "a" and "b" when all I have are the variances?
If I know the variance on a and b, what is the variance on y?
I know that generally, sigma_y^2 = (dy/da)^2*sigma_a^2 + (dy/db)^2*sigma_b^2. But, what I don't understand is with this nonlinear equation, my partial derivatives are still a function of a and b respectively. So, if I have:
sigma_y^2 = 4a^2*sigma_a^2 + 4b^2*sigma_b^2 (assuming covariance is 0),
what do I use for "a" and "b" when all I have are the variances?