I have exponential distributed data $Exp(\lambda)$ with sample n = 50. Also, The sample mean = 2.17. I need to find the estimator of parameter $\lambda$ by the method of moments and to build 95% confidence interval.
We know, that by the method of moments we got the estimation the parameter $\lambda$ = $1/\bar X$.
Now for confidence interval of my estimator i must calculate the variance of estimator: $Var(\hat \lambda)$ = $Var(1/\bar X)$
But now i am not sure what to do. My attempt: $1/Var(\bar X) = 1/Var(\sum (1/n) *X_i)$ and by the propery o variance i got the result $\lambda^2 * n$.
But i doubt, that is correct result. Can you please help me? many thanks