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For a random sample of size $n$ drawn from a Pareto distribution with parameter $\theta=5,000$, an estimator for $\theta$ is \[ \hat{\theta}=5,000 \cdot \frac{n}{n+1} \] Which of the following statements are true about the estimator $\hat{\theta}$ ? I. $\hat{\theta}$ is an unbiased estimator of $\theta$. II. $\hat{\theta}$ is a consistent estimator of $\theta$. III. When $n=10$, the mean squared error of $\hat{\theta}$ is more than 200,000 . A None are true B I and II only c I and III only D II and III only E $1, \mathrm{II}$, and III

For a random sample of size $n$ drawn from a Pareto distribution with parameter $\theta=5,000$, an estimator for $\theta$ is \[ \hat{\theta}=5,000 \cdot \frac{n}{n+1} \] Which of the following statements are true about the estimator $\hat{\theta}$ ? I. $\hat{\theta}$ is an unbiased estimator of $\theta$. II. $\hat{\theta}$ is a consistent estimator of $\theta$. III. When $n=10$, the mean squared error of $\hat{\theta}$ is more than 200,000 . A None are true B I and II only c I and III only D II and III only E $1, \mathrm{II}$, and III

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