Question: Prove the following statement. LetYbe uniformly distributed on [0,1]. Then, for any >0, there exists a random variableXsuch that (a) X FSD Y; (b)P(XY) =

Prove the following statement.

LetYbe uniformly distributed on [0,1]. Then, for any >0, there exists a random variableXsuch that

(a) XFSDY;

(b)P(XY) = 1- .

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