If $X_{1}, X_{2}, \ldots, X_{n}$ constitute a random sample of size $n$ from an exponential population, show that $\vec{X}$ is a consistent estimator of the parameter $\theta$.
Added by Leslie B.
Step 1
The exponential distribution is defined as $f(x|\theta) = \frac{1}{\theta}e^{-x/\theta}$ for $x > 0$ and $\theta > 0$. The parameter $\theta$ is the mean (or expected value) of the distribution. Show more…
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