Consider a sequence of independent random variables (left{X_{n}ight}_{n=1}^{infty}) where (X_{n}) has a (operatorname{Binomial}(1, theta)) distribution. Prove that

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Consider a sequence of independent random variables $\left\{X_{n}ight\}_{n=1}^{\infty}$ where $X_{n}$ has a $\operatorname{Binomial}(1, \theta)$ distribution. Prove that the estimator

\[\hat{\theta}_{n}=n^{-1} \sum_{k=1}^{n} X_{k}\]

is a consistent estimator of $\theta$.

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Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

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Question Posted: Mar 15, 2024 02:00 AM

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Consider a sequence of independent random variables (left{X_{n}ight}_{n=1}^{infty}) where (X_{n}) has a (operatorname{Binomial}(1, theta)) distribution. Prove that

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Introduction To Statistical Limit Theory

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