In question, we have been asked to calculate "large-sample approximate variance" (i.e. CRLB) for MLE of exponential distribution. But since MLE of exp distribution is a "Biased Estimator" as E(1/X-bar) = Lambda × n / n-1, how can CRLB be calculated for it ? Doesn't CRLB only apply for unbiased estimator ? The Unbiased Estimator would be (n-1/n) x (1/X-bar). The difference between estimates under both is too big to igonre, due to small sample size of 20 in question. (Biased estimate = 0.11494 and Unbiased estimate = 0.1092)
Fair point. Although for large samples it does approach the unbiased results - this won't be the case here. However, for a paper based exam we are limited. We'd actually use a parametric bootstrap to calculate this accurately.
