In this section we prove a technical lemma that is needed for the proof of Lemma 3.4.
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It is easy to check that is indeed a distribution over
(with support set
).
Let and
be independent random variables from distributions
and
, respectively. Now define
as follows:
We claim that the such defined is suitable. Indeed, by Equation
13
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Furthermore,
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We calculate each term of Equation 14 separately, both for
and
. First assume that
. Then
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Now let us consider the case .
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In both cases we get
, which was to be proven.