Question:

Using Chebyshev’s Inequality show that if \[{{\hat{\theta }}_{n}}\] is an unbiased estimator of \[\theta \] and the \[{{\lim }_{n\to \infty }}Var({{\hat{\theta }}_{n}})=0\] then \[{{\hat{\theta }}_{n}}\] is a consistent estimator of \[\theta \] .

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