Showing a limited preview of this publication:
Abstract
We study the distribution of a random variable
where ηk are independent random variables having the distributions: 
, P{ηk = 1} = p1k ≥ 0, 
. We prove that the r.v. ξ has either pure discrete (atomic) or pure continuous distribution. In the case of discreteness of the r.v. ξ, we describe the set of all its atoms. For the continuously distributed r.v. ξ, we give the formula for the distribution function and prove the criterion for singularity of Cantor type.
Key words.: Random variable; random continued fraction with independent elements; A2-continued fraction; purity of the probability distribution; singularly continuous probability distribution of Cantor type
Received: 2008-04-04
Published Online: 2009-05-29
Published in Print: 2009-May
© de Gruyter 2009
