Course design: basics first or teach "as you go"
I assume you know your students better than I do, but this would depend to a certain amount on what sorts of things they expect. At base, it seems like they are expecting/wanting a course in robotics. Starting out with something different might disappoint them and turn them against you in a way that could be hard to &quot;make up&quot; later. This implies doing statistics/probability &quot;just in time&quot;.
However, students who are used to, and comfortable with, highly theoretical courses might be fine with &quot;basics first.&quot;
But another alternative is to give them, early on, a set of readings on probability that you advertise as being essential a bit later in the course, while you focus on the robotics part. The better students might spend some time scanning, at least, those readings, making it easier to do the probability stuff when it becomes essential. You might even be able to find a vehicle for responding to questions on the readings without cutting too much into the time you spend on robotics early on.
And, of course, if their expectation is that robotics is just &quot;applied probability&quot; then theory first would likely be better.
But, think first of the student expectations and work to satisfy that as much as is reasonable.