Distribution of Geometrically Weighted Sum of Bernoulli Random Variables

Deepesh Bhati, Phazamile Kgosi, Ranganath Narayanacharya Rattihalli

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DOI: 10.4236/am.2011.211195                

Abstract

A new class of distributions over (0,1) is obtained by considering geometrically weighted sum of independent identically distributed (i.i.d.) Bernoulli random variables. An expression for the distribution function (d.f.) is derived and some properties are established. This class of distributions includes U(0,1) distribution.

Keywords

Binary Representation, Probability Mass Function, Distribution Function, Characteristic Function

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Kunte and R. N. Rattihalli, “Uniform Random Variable. Do They Exist in Subjective Sense?” Calcutta Statistical Association Bulletin, Vol. 42, 1992, pp. 124-128.
[2]	K. L. Chung, “A Course in Probability Theory,” 3rd Edi-tion, Academic Press, Cambridge, 2001.