Need help understanding some probability stuff..

1. When would I know if a question is asking for PDF,CDF or PMF? Any "red flags" on when i should calculate them?

2. What are the ways to calculate moments? I understand in continuous i need to take the derivative of the Laplace transform of the PDF? Or can I just take the derivative of the PDF? What about moments for discrete values/functions?

3. What are the ways to calculate variances and when to use what? I know the normal way is Var[X] = E[X^2] - E[X]^2 but what about other ways for non continuous like sums like binomial or others?

4. What do i do if i want to add 2 PDFs together? I think i do convolution?

5. When do I know i should calculate distribution with Binomial, Normal, PDF/laplace etc.? Any hints/red flags that shows to use one over the other? And how do i calculate the cdf if it is a summation not continuous?
thanks!

You'r asking very general basic info in probability. It may be a better idea to read more and ask if you got stuck somewhere. You can start from here:
Probability density function - Wikipedia, the free encyclopedia

The difference between pdf and cdf is *very* obvious, very simple.


If I were you, I start with a simplest continuous dist, say Uniform, and calculate all that you were asking, cdf, MGF, Mean, E(X^2), variance, ... and all, as given here:
http://en.wikipedia.org/wiki/Uniform...on_(continuous)

- O, reading is not a bad thing, but it takes time :)