  Bernoulli sieve is a recursive construction of a random composition (ordered
partition) of integer $n$. This composition can be induced by sampling from a
random discrete distribution which has frequencies equal to the sizes of
component intervals of a stick-breaking interval partition of $[0,1]$. We
exploit Markov property of the composition and its renewal representation to
derive asymptotics of the moments and to prove a central limit theorem for the
number of parts.
