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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.
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