The following is an experiment with, 1000, random  words in the alphabet,

    {1, 2}, that add-up to, 100

and finding the empirical average, standard deviation, and scaled moments up\

     to the, 6, -th

         accodring to the random  variable: number of occurrences of, 1

It also outputs the exact values (theorerically derived) for the averge and \
    standard deviation

[44.88800000, 5.774725621, 0.07568140355, 3.083518275, 1.116843896, 15.78255840

    ], [44.96857316, 5.984551657]

                          This took, 4.145, seconds .