First 3 definitions:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{array}{l}

\left( 1 \right)\mathop {\lim }\limits_{n \to \infty } P\left( {\left| {X_n - X} \right| > \varepsilon } \right) = 0 \\

\left( 2 \right)P\left( {\mathop {\lim }\limits_{n \to \infty } X_n = X} \right) = 1 \\

\left( 3 \right)\mathop {\lim }\limits_{n \to \infty } E\left[ {\left( {X_n - X} \right)^2 } \right] = 0 \\

\end{array}

[/tex]

I need to find:

a. an example that (1) does not give (3).

b. an example that (1) does not give (2).

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# Limit definition examples

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