Geodesic
On properties of binary random numbers
Applications of Mathematics, Tome 19 (1974) no. 6, pp. 375-385

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Let $\{X_k\}^\infty_{k=1}$ be a sequence of independent zero-one random variables (rv) with $P(X_k=1)=\frac{1}{2} + \Delta$. Then we define the binary random number (brn) $Y=\sum^\infty_{k=1} X_k2^{-k}$. An ideal generator produces 0 and 1 with equal probability, but a real one does it only approximately. The purpose of this paper is to find distribution of brn for $-\frac{1}{2}\Delta \frac{1}{2}$ (also $\Delta =\Delta_k$). Particularly, convergence of the normed sum of brn to normally distributed rv is studied by means of Edgeworth expansion.
Let $\{X_k\}^\infty_{k=1}$ be a sequence of independent zero-one random variables (rv) with $P(X_k=1)=\frac{1}{2} + \Delta$. Then we define the binary random number (brn) $Y=\sum^\infty_{k=1} X_k2^{-k}$. An ideal generator produces 0 and 1 with equal probability, but a real one does it only approximately. The purpose of this paper is to find distribution of brn for $-\frac{1}{2}\Delta \frac{1}{2}$ (also $\Delta =\Delta_k$). Particularly, convergence of the normed sum of brn to normally distributed rv is studied by means of Edgeworth expansion.
DOI : 10.21136/AM.1974.103555
Classification : 60F05, 60F99, 65C10 
Víšek, Jan Ámos. On properties of binary random numbers. Applications of Mathematics, Tome 19 (1974) no. 6, pp. 375-385. doi: 10.21136/AM.1974.103555
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