Question: Let X and Y be independent and identically distributed random variables with 0 0. Show that Pz = Px implies (i) a = v2, (ii)

Let X and Y be independent and identically distributed random variables with 0 0. Show that Pz = Px implies (i) a = v2, (ii) (ex(x/2" )) 23m = Yx(x) for all r E R and n E N, (iii) X ~ N(0, Var(X))

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