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?