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When constructing uniform random numbers in [0, 1] from the output of a physical device, usually n independent and unbiased bits B
j
are extracted and combined into the machine number
. In order to reduce the number of data used to build one real number, we observe that for independent and exponentially distributed random variables X
n
(which arise for example as waiting times between two consecutive impulses of a Geiger counter) the variable U
n : = X
2n – 1/(X
2n – 1 + X
2n
) is uniform in [0, 1]. In the practical application X
n
can only be measured up to a given precision (in terms of the expectation of the X
n
); it is shown that the distribution function obtained by calculating U
n
from these measurements differs from the uniform by less than /2.We compare this deviation with the error resulting from the use of biased bits B
j
with P
{B
j
= 1{ =
(where ] –
[) in the construction of Y above. The influence of a bias is given by the estimate that in the p-total variation norm Q
TV
p
= (
|Q()|
p
)1/p
(p 1) we have P
Y
– P
0
Y
TV
p
(c
n
· )1/p
with c
n
p
for n . For the distribution function F
Y
– F
0
Y
2(1 – 2–n
)|| holds. 相似文献
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