This course is (the higher counterpart of) one of the core courses for a major in statistics. Inference is essentially concerned with the decision making in statistics. The aim is to be able to construct and then use the most optimal tests for a much greater variety of scenarios, as opposed to the one or two special cases covered in MATH2901.
This course completely surpassed my expectations. I went in not expecting much but despite the lack of past papers, Spiro clearly knows how to manage/teach a course. Assessments were definitely doable and I doubt I can achieve such a result again.
I had an interesting experience with this course. Assignment 1 was released, I'd learn up to everything needed for it, and then be too tired to continue. Midterm starts looming, I learn everything up to that point, and then be too tired to do more. Assignment 2 released, same thing happens. (And then of course finals come and I need to know the entire syllabus.) Moral of this story though is that it's perfectly possible to do well in this course provided you stay on track when you need to. There's quite a fair bit that gets asked and at times I got confused easily (much like in MATH3871), but so long as you know what you need when you actually need it, it's mostly fine.
Some remarks: I think bootstrapping/jacknifing/robustness doesn't really pop up in exams - only assignments. (Doesn't mean you should purposely ignore them obviously, but if you're running short on time, well you know what to prioritise.) The Bayesian inference part only goes for one week and definitely not anywhere in depth as with MATH3871 - having done that course first made that week easy for me. Also I think actuarial students do have an edge, having seen a lot of the tests already (Wilcoxon, Kolomogorov-Smirnov, chi-squared GoF etc.)
Also, definitely try to keep on track with the lectures