S2 confusion

Your first statement is correct.

However for your second statement, if your cdf is F then what you're suggesting is to solve F(x)=1/2. This would give you the median value of your random variable, not the expectation. What you need to do instead is to differentiate F with respect to x to get the pdf f. Then integrate xf(x) with appropriate limits to get the expectation.

just to clear things up:

pdf: integrate xf(x) with limits
cdf: differentiate to get pdf, THEN integrate xf(x) with limits?

if so, that makes perfect sense. thanks a lot