Sampling with replacement covers ~63.2% of source data

sampling_with_replacement.py

In [1]: import random

In [2]: import numpy as np

In [3]: SIZE = 1000000

In [4]: data = range(SIZE)

In [5]: results = []

In [6]: for run in xrange(1, 101):
    ...:     counts = {}
    ...:     for i in xrange(SIZE):
    ...:         item = random.choice(data)
    ...:         counts[item] = counts.get(item, 0) + 1
    ...:     results.append(len(counts))
    ...:     print "Run %s: %s (avg %s, %s%%)" % (run, len(counts), np.average(results), 100.0 * np.
    ...: average(results) / SIZE)
    ...:     
    ...:     
Run 1: 632137 (avg 632137.0, 63.2137%)
Run 2: 632020 (avg 632078.5, 63.20785%)
Run 3: 631915 (avg 632024.0, 63.2024%)
Run 4: 631839 (avg 631977.75, 63.197775%)
Run 5: 632021 (avg 631986.4, 63.19864%)
Run 6: 631660 (avg 631932.0, 63.1932%)
Run 7: 632454 (avg 632006.571429, 63.2006571429%)
Run 8: 632607 (avg 632081.625, 63.2081625%)
Run 9: 631580 (avg 632025.888889, 63.2025888889%)
Run 10: 631856 (avg 632008.9, 63.20089%)
Run 11: 632433 (avg 632047.454545, 63.2047454545%)
Run 12: 632293 (avg 632067.916667, 63.2067916667%)
Run 13: 632303 (avg 632086.0, 63.2086%)
Run 14: 632373 (avg 632106.5, 63.21065%)
Run 15: 631974 (avg 632097.666667, 63.2097666667%)
Run 16: 632207 (avg 632104.5, 63.21045%)
Run 17: 632368 (avg 632120.0, 63.212%)
Run 18: 632355 (avg 632133.055556, 63.2133055556%)
Run 19: 631806 (avg 632115.842105, 63.2115842105%)
Run 20: 631754 (avg 632097.75, 63.209775%)
Run 21: 631686 (avg 632078.142857, 63.2078142857%)
Run 22: 632017 (avg 632075.363636, 63.2075363636%)
Run 23: 632130 (avg 632077.73913, 63.207773913%)
Run 24: 632147 (avg 632080.625, 63.2080625%)
Run 25: 632068 (avg 632080.12, 63.208012%)
Run 26: 631961 (avg 632075.538462, 63.2075538462%)
Run 27: 631866 (avg 632067.777778, 63.2067777778%)
Run 28: 632078 (avg 632068.142857, 63.2068142857%)
Run 29: 632384 (avg 632079.034483, 63.2079034483%)
Run 30: 631649 (avg 632064.7, 63.20647%)
Run 31: 632279 (avg 632071.612903, 63.2071612903%)
Run 32: 632408 (avg 632082.125, 63.2082125%)
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Run 35: 631973 (avg 632091.742857, 63.2091742857%)
Run 36: 632245 (avg 632096.0, 63.2096%)
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Run 39: 631538 (avg 632112.974359, 63.2112974359%)
Run 40: 632874 (avg 632132.0, 63.2132%)
Run 41: 631764 (avg 632123.02439, 63.212302439%)
Run 42: 631965 (avg 632119.261905, 63.2119261905%)
Run 43: 632068 (avg 632118.069767, 63.2118069767%)
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Run 50: 632392 (avg 632115.3, 63.21153%)
Run 51: 632253 (avg 632118.0, 63.2118%)
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