 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

For any $\lambda>0$, the variable $Z=|X_1|/\lambda$ has infinite expectation. Part (a)(ii) therefore forces $\sum_n\mathbb P(|X_1|\geq\lambda n)=\infty$. Identical distributions give
$$
\boxed{\sum_n\mathbb P(|X_n|\geq\lambda n)=\infty.}
$$

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