I am an MS student in applied math. I have studied a lot on probability theory, stochastic processes, Bayesian theory and subjects related these areas. However, when I got to a point to really implement all those theory into action and really do solve a real-world problem I just figured out that I am far away from doing such. For example I wasn't aware about preparing my data, raw observation principles and things like that on samples that I work on.
Even worse than that, with all those distribution functions and their properties in my head, I could not relate and give an inference for my choice of a distribution for a sample. I had also learnt some languages like c,c++, Matlab, but can't really use them in this area.
SO I decided to learn very basic and practical materials about working with data, like distribution fitting, preparing samples, using programs like R, and anything that one needs to solve a real-world problem using empirical and observation data. Therefore I am asking for help on introducing me to reliable sources, lecture notes, books, websites, languages, anything that is essential to get around these subject. I really have only 6 months to learn these in a way to be able to implement them on my data that I have started collecting them.
I really appreciate any help from you people.