[int3]

I'm currently doing MITx's Fundamentals of Statistics MOOC, which seems fairly similar to this one. The course material doesn't require too much understanding of real analysis, though the instructor does make cursory acknowledgements of the "technical details" he's glossing over, presumably for the more advanced students. The only analysis concepts we've used are continuity, differentiability, and convergence. It isn't a proof-based course: the instructor does prove some theorems in class, but the psets are all just computation. I do agree that it'll be harder to internalize some of the concepts w/o a background in analysis, but I think you can get a reasonable amount out of the course regardless.

That said, I did study analysis (but not measure theory) in college, and I don't entirely remember what I learned from calc vs analysis classes, so I may be a bit off here.