Consider a variation of the binomial random walk.
In the traditional binomial random walk, each step has a consistent step size (let's assume this size is 1), and there's an equal probability of moving either to the left or the right. We can represent this as:
${\displaystyle {S = X_{1} + X_{2} + ... + X_{n}}}$
where $X_{i}$ are independent and identically distributed (iid) random variables.
In our modified version of the binomial random walk, the step sizes differ.
What would the distribution look like for this modified binomial random walk? It this distribution related to some well-known distribution ?