The complete set in the coupon collector's problem consists of all 
possible types of object. For a positive
integer 
,
suppose successive draws are independent
and identically distributed and follow the discrete
uniform distribution on these types. The expectation
value of the number of draws needed to collect every type is 
, where 
is a harmonic number
(Havil 2003, p. 131). For 
, 2, ..., the first few values are therefore 1, 3, 11/2,
25/3, 137/12, 147/10, 363/20, ... (OEIS A096617
and A027611).
Complete Set
See also
Coupon Collector's Problem, Harmonic NumberExplore with Wolfram|Alpha
References
Havil, J. "Collecting a Complete Set." §13.9 in Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, pp. 130-131, 2003.Sloane, N. J. A. Sequences A027611 and A096617 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Complete SetCite this as:
Weisstein, Eric W. "Complete Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompleteSet.html