(* Simulation << Knox7/Util *)



StepSize[p_] := If[RandomReal[] <= p, 1, -1]



SimulatedRandomWalk[p_, n_, M0_] := 

 Module[{statelist, done, currstate, nextstate}, 

  statelist = {n}; 

  currstate = n; 

  done = (currstate <= 0) || (currstate >= M0);

   While[Not[done], 

   nextstate = currstate + StepSize[p]; 

   AppendTo[statelist, nextstate];

   currstate = nextstate;

   done = (currstate <= 0) || (currstate >= M0)];

  statelist]









thewalk = SimulatedRandomWalk[0.5, 4, 8]

ListPlot[thewalk, PlotStyle -> {PointSize[.015], Blue}]

ListLinePlot[thewalk, PlotStyle -> {PointSize[.015], Blue}]