Random walk, discrete time, 1D, unequal discrete steps

Question

Can someone point me towards a resource that will help me analyse a 1-d random walk where each step can take 1 of say 6 values with known probabilities. Not a continuous time random walk, time intervals are discrete and equal.

Answer 1

You can replace the step length by its expected value (a constant).

The randomness of the walk and the size of the step are assumed to be independent.