Probability mass function (piecewise function) Cant post image due to reputation, posted in comments
Here is a probability mass function and probabilities computed (from a past test). I am confused on the notation of $F(x-)$ - I am assuming it means like a limit and approaching from one side. Why is this being used, especially in questions b, c, and e? For example with e, Why is $P(X=1)$ not just $F(1)$?

The distribution function $F$ is the cumulative distribution function, not the probability mass function or the probability density function. It is defined by $F(x) = \mathbb{P}(X \le x)$.
I am assuming $F(x-)$ denotes $\lim_{t \nearrow x} F(t)$, where the limit is for $t$ approaching $x$ from below. You may want to convince yourself that $F(x-) = \mathbb{P}(X<x)$ (in contrast with $F(x) = \mathbb{P}(X \le x)$).
