I'm not familiar with probability.
Say I have some n data points over the reals $\{x_i\}_{i=1}^n \subset \mathbb{R}$ such as the distance to the basket during a field goal attempt. How should I construct a distribution over the real line to fit this data?
Say I pick the normal distribution (not sure about the connection to the data). How can I measure the probability that a new data point z will exist according to my distribution?
Certainly, to get a positive probability, I must pick a neighborhood around the data point. But my probability then depends on the width of the neighborhood...
Do I need to make the domain discrete?