Though i think pdfs are useful, they may be a bit advanced.

Perhaps linking integrals/derivatives into stats could be done from a more discrete approach as opposed to a continuous one first.

For example: Starting with a representation of an integral as sum of areas of rectangles (something most students can do) and then saying what happens if the width of all the rectangles gets smaller and smaller. A la Riemann

This could then tie into the pdf quite reasonably?