Chapter 9.7, Problem 81E

Suppose that Y₁, Y₂, …, Y_n denote a random sample from an exponentially distributed population with mean θ. Find the MLE of the population variance θ². [Hint: Recall Example 9.9.]

EXAMPLE 9.9 Let Y₁, Y₂, …, Y_n denote a random sample from the exponential density function given by

$f(y|\theta )=\{\begin{array}{ll}\left(\frac{1}{\theta }\right)e^{-y/\theta },\hfill & y>0,\hfill \\ 0,\hfill & \text{elsewhere}.\hfill \end{array}$

Find an MVUE of V (Y_i).