
06332884
j
2014f.00824
Murphree, Emily S.
Replacement costs: the inefficiencies of sampling with replacement.
Math. Mag. 78, No. 1, 5157 (2005).
2005
Mathematical Association of America (MAA), Washington, DC
EN
K65
sampling with replacement
Markov chain
Bernoulli random variables
random number generator
doi:10.2307/3219274
Summary: When a sample is chosen with replacement, the same item may be chosen several times. The number of distinct items appearing in the sample is a random variable whose properties are explored in this paper. To avoid combinatorial difficulties, the distribution of the number of distinct items is derived by using a Markov chain approach. Expected values are derived from simple properties of Bernoulli random variables. Finally, the distributional results are used to test a random number generator.