What's the name of a random variable that takes on values of either 0 or $i$ with probabilities $p$ and $1-p$, respectively?
The mathematics is almost identical to Bernoulli Random Variables, but I can't find what the name of this would be.
Thanks for the help!
It's a type of indicator variable. Let $1_A$ be the random variable for which $1_A(\omega)=1$ if $\omega\in A$ and 0 otherwise, where $A$ is an event. Then your random variable can be described as $i1_A$. It's equal to $i$ if $\omega\in A$, which happens with probability $P(A)$, and 0 otherwise, which happens with probability $1-P(A)$.