Let X N.o), Y N(,0), and U Uniform(0, 1) such that U and (X,Y) are independent....

 

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Let X N.o), Y N(₂,0), and U Uniform(0, 1) such that U and (X,Y) are independent. For a given constant a € (0,1), define the new random variable Z -{} X if Usa, Y otherwise. Let (-) denote the distribution function of a standard normal random variable. Find the distribution function of Z Let X N.o), Y N(₂,0), and U Uniform(0, 1) such that U and (X,Y) are independent. For a given constant a € (0,1), define the new random variable Z -{} X if Usa, Y otherwise. Let (-) denote the distribution function of a standard normal random variable. Find the distribution function of Z

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