How to tackle a statistics problem given a random variable X? I'm having trouble getting an overall grasp of certain aspects of statistics, namely knowing when to use which formula/approach to solve a problem.
Let's consider a random variable X, after you determine whether the random variable is continuous or discrete, how would you know whether to know whether to use a binomial distribution, exponential distribution, Poisson distribution, moment generating function, etc.?
For example, I know that if I'm asked to model the time between random events I know I have an exponential distribution problem.
It's just that there are so many different mean, variance, and other equations, I got lost along the way on which equation to apply where. Some clarification would be great.
 A: I am not really qualified to answer this question since I am a topologist, but I think it really depends on the analytical nature of your problem instead of judging from its behavior mathematically alone. There are surprising applications of various distributions to problems in real life, but that usually comes with an understanding of the phenomenon first. 
A classic in this regard is Feller's book, in which almost no statement is proposed without an applied "example" at mind. You probably can find the book in your local library. 
A: The first step is to thoroughly understand the scenario that is being described, and  what quantity the random variable represents.  Each of the common distributions has a typical paradigm for what it represents.  For example, the binomial distribution would represent the number of "successes" in a fixed number of independent trials.  On the other hand a hypergeometric distribution also represents the number of "successes", but where you're selecting a fixed number of objects selected without replacement from a given population.
