Suppose there is a random variable $X$ that can take on values $-1,0,1$, with probabilities $P(X=1)=P(X=-1)=.25$ and $P(X=0)=.5$.
How can I work with such a random variable in mathematica? (Find the mean, transform it -- for example by adding it to another random variable -- etc).
EmpiricalDistribution command seems to do this, but creates a
DataDistribution instead of distribution.
So my question is whether using
EmpiricalDistribution is the correct way to model such a random variable, and if so is there downfalls/issues that
DataDistribution objects have that typical distributions dont? (For example, perhaps they are much slower?)
(Aside: Instead of a random variable $X$ taking on 3 values, a more practical example is perhaps a distribution for a "weighted/damaged" dice that has $0$ probability of showing 6, and $1/3$ probability of showing 1)