Confidence interval Concept Check

1 point possible (graded)

As in the previous section, let X1,,Xniidexp(). Let

n:=nni=1Xi

denote an estimator for . We know by now that n is a consistent and asymptotically normal estimator for .

Recall q/2 denote the 1/2 quantile of a standard Gaussian. By the Delta method:

[nq/2n,n+q/2n]=:I

with probability 1. However, I is still not a confidence interval for .

Why is this the case?