(* To Successively Simulate Sample Values from a Given Distribution *)



SimMeanSequence[distribution_, nummeans_, m_] :=

 Module[{nextsample, meanlist, runningsum, currnumobs},

  currnumobs = 0; runningsum = 0;

  meanlist = {};

  While[currnumobs < nummeans,

   nextsample = RandomReal[distribution, m];

   currnumobs = currnumobs + m;

   runningsum = runningsum + Plus @@ nextsample;

   AppendTo[meanlist, runningsum/currnumobs]];

  ListPlot[meanlist, PlotStyle -> PointSize[0.02], Joined -> True]]





(* Plot of Sample Means *)



SeedRandom[235711]

SimMeanSequence[GammaDistribution[2, 3], 2000, 10]