Sankhya-The Indian Journal of Statistics Series B, 31 (Dec), 413-420
ISSN / ISBN: 0581-5738
SUMMARY: This paper finds the distribution of the most significant digit of some functions of random variables X1, X2, … , Xn, where these variables are independent and distributed uniformly in (0, 1). The probability that the most significant digit of Yn is A (A=1, … , 9) has been found, where Yn is defined as the products of the reciprocals of n such random variables. It has been shown that this probability tends to log10(A+1)/A as n tends to infinity. Similarly if Zn is defined as Zn=X1/X2/… /Xn+1, it has been proved that the probability distribution of the most significant digit of Zn also tends to log10(A+1)/A as n tends to infinity. More generally, it is found that if V1, V2, … , Vn are defined as V1=B/X, … , Vn=Vn-1/Xn where B is any random variable defined on the positive axis of the real line, the probability distribution of the most significant digit tends to log10(A+1)/A as n tends to infinity
Bibtex not available at this time.
Reference Type: Journal Article
Subject Area(s): Probability Theory