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Question 1: Let ( Y n , n 0 ) be a sequence of i.i.d. random variables, all uniform on [ 0 , 1 ] and
let X n = 1 ( Y n 1/ n ) . Show that X n 0 in probability but not almost surely.

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  • 1. Question 1: Let ( Y n , n 0 ) be a sequence of i.i.d. random variables, all uniform on [ 0 , 1 ] and let X n = 1 ( Y n 1/ n ) . Show that X n 0 in probability but not almost surely.