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Standard normal random variable

Suppose that Y is generated using this method and U3 is another Unif(0,1) random variable. Define the random variable Z asZ=Y if U3 > 0.5Z=-Y if U3 <=0.5Show that Z is a standard normal random variable.Q. I Consider the following rejection algorithm1 . Generate ? independent Unif ( 0 , 1 ) random variables U , and U/} .2. Let * = _ In V' , and Y = _ In U 2.3. IF 2 X > ( 7 - 1) 2 return Y.

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