Can different departments offer similar courses?
There are a number of reasons why a department would want to teach their own version of a class, even if it's very similar to a course taught by another department:


They think they can do it better. Imagine if most graduate students in your Department A end up taking a class in Department B. Department B views this as something of an imposition, not really interesting, not taken by many of their students, etc. so treats it as a dumping ground for new or poor teachers. Department A might decide to teach their own version to the level they think it warrants.
Different audiences. What one needs to know may differ by department in terms of sophistication or focus. For example, very few students in departments who use statistical methods might need to know the nuances behind how variance is calculated, or be equipped with the background to develop their own estimator, whereas a student in a statistics department might very well need to. Splitting these courses allows for fine-tuning of content and pre-requisites (do you need to know Linear Alegbra?).
Field specific focuses. Epidemiology, as a field, is by and large uninterested in prediction for its own sake, and so really doesn't do much with machine learning (see here). Other fields are keenly interested in exactly those methods. So rather than try to teach a course that's a little unsatisfactory to everyone, why not split them? Similarly, while an Applied Math department could very well teach a class on "Mathematical Modeling", the assumptions and methods needed in Physics vs. Chemistry vs. Ecology vs. Epidemiology vs. Engineering are all different enough that those departments might be well served by bringing their class in house, if for no other reason than to make sure most of the examples are relevant.
Geography. As @tomasz points out, the "logical" department for a course to be held in might be quite far from a department, leading to students not taking a class, not knowing about it entirely, or complicating their schedule. For example, a statistics or math department might be on the "main" Liberal Arts campus of a university, while many of the potentially interested students may be located on a specialized Health Sciences campus a considerable distance away (at the University of Iowa, for example, they would be across the Iowa River from one another).