Distribution of Geometrically Weighted Sum of Bernoulli Random Variables

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.

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

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

Cite this paper

nullD. Bhati, P. Kgosi and R. Rattihalli, "Distribution of Geometrically Weighted Sum of Bernoulli Random Variables,"*Applied Mathematics*, Vol. 2 No. 11, 2011, pp. 1382-1386. doi: 10.4236/am.2011.211195.

nullD. Bhati, P. Kgosi and R. Rattihalli, "Distribution of Geometrically Weighted Sum of Bernoulli Random Variables,"

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.

[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.