Chapter 8.4, Problem 37E

Refer to Exercise 8.36. An engineer observes n = 10 independent length-of-life measurements on a type of electronic component. The average of these 10 measurements is 1020 hours. If these lengths of life come from an exponential distribution with mean θ, estimate θ and place a 2-standard-error bound on the error of estimation.

8.36 If Y₁, Y₂, … , Y_n denote a random sample from an exponential distribution with mean θ, then E(Y_i) = θ and V (Y_i) = θ². Thus, $E(\bar{Y})=\theta$ and $V(\bar{Y})={\theta }^2/n$, or ${\sigma }_{\bar{Y}}=\theta /\sqrt{n}$. Suggest an unbiased estimator for θ and provide an estimate for the standard error of your estimator.