- #1
Zaare
- 54
- 0
First 3 definitions:
[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).
[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).