Asymptotic Distribution/Examples/Arbitrary Example 1
Example of Asymptotic Distribution
Let $X_1, X_2, \ldots, X_n$ be $n$ independent observations from a probability distribution with expectation $\mu$ and finite variance $\sigma_2$.
Then $Y_n = \ds \sum_{k \mathop = 1}^n X_k$ has expectation $n \mu$ and variance $n \sigma_2$.
Both of these tend to infinity, unless $\mu = 0$.
Proof
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