First of all, apologies for my poor terminology - I have a particular problem which I understand in own terms, but I am having difficulty in applying the mathematics in the correct manner.
My problem is that I have a point in 2D space with an uncertainty in two directions. These directions happen to be perpendicular to one another, however they are not necessarily perpendicular to the axes. (If it helps, the point represents a top-down view of an object from an image - there is uncertainty horizontally in the image as well as a larger uncertainty in the depth of the object). I can find the standard deviation of the two components and represent them as univariate distributions, but I'd instead like to represent them as a 2D distribution as they should be.
I can completely see that this is possible and probably very simple but I just can't quite make the leap from my visualisation of the problem to the mathematical formalism - I only need to calculate the parameters of the 2D distribution (specifically, I guess, the covariance - I know the mean). If someone could just give me a prod in the right direction I would be very grateful.