Rubyで使用されている乱数の均等分布について(メルセンヌ・ツイスタ) ref: http://qiita.com/kozakana/items/b5229094cf8d29767847

MT_Average.rb

MAX_VAL = 101
REP_CNT = 10**6

sum = 0.0
prng = Random.new(Random.new_seed)
(0...REP_CNT).each{|idx|
    p sum = (sum*idx + prng.rand(MAX_VAL))/(idx+1)
}

MT_AverageGraph.rb

# -*- encoding: utf-8 -*-

require 'rubygems'
require 'gruff'

FONT = "/Library/Fonts/Osaka.ttf"
MAX_VAL = 101
GRAPH_NUM = 7
REP_CNT = 10**GRAPH_NUM

graph_point = Array.new(GRAPH_NUM)

avg, rec_cnt = 0.0, 0
prng = Random.new(Random.new_seed)
(0...REP_CNT).each{|idx|
    avg = (avg*idx + prng.rand(MAX_VAL))/(idx+1)
    if 10**rec_cnt-1 == idx
        graph_point[rec_cnt] = avg
        rec_cnt += 1
    end
}

p graph_point

g = Gruff::Line.new
g.font = FONT

(0..graph_point.length).each{|idx|
    g.labels[idx] = "10^#{idx}"
}

g.data("Mersenne twister", graph_point)
g.write('MT.png')

MT_AverageGraphNum.rb

実際の値は
10^0:67.0
10^1:55.5
10^2:52.39
10^3:51.352
10^4:50.076400000000085
10^5:49.93751999999963
10^6:49.99161700000036
10^7:49.99675620000007