Could someone explain what comes from pdf and what comes from cumulative distribution function (cdf) as far as: Probabilities ( $x < a,$ or $a < x < b$), standard deviation, Expected value, and variance?
Edit: to elaborate on what I've tried and where I am having a lapse in understanding,
I understand you can go from pdf to cumulative distribution function by taking the integral from negative infinity to infinity.
But once I have both, I'm having difficulty calculating probabilities, standard deviation and the mean due to not knowing when to use pdf vs cdf to calcuate it.
for example: to get the probability of x being between A and B, do I integrate from A to B the pdf dx, or do I integrate from A to B the cdf dx