Suppose X1, . . . , Xn are independent and exponential with parameter θ. Let p me an estimator such that p = #{i : Xi > 1}/n Where #A is the number of of elements in A.
The original question is to find the asymptotic efficiency but part of it requires me to find the asymptotic variance of -log p. I know I need to find the expectation of p and then use the delta method to find the Asymptotic variance but am struggling to find the expectation.