Let X 1 , X 2 , , X n be a random sample of size n from a distribution that is N(, 2 ), where 2 0 Show that the sum Z n n 1 X i does not have a limiting distribution

Question: Let X 1 , X 2 , . . . , X n be a random sample of size n from a distribution that is

Let X₁, X₂, . . . , X_n be a random sample of size n from a distribution that is N(μ, σ²), where σ² > 0. Show that the sum Z_n =Σⁿ₁ X_i does not have a limiting distribution.

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