Question

Confidence interval Concept Check

1 point possible (graded)

As in the previous section, let X1,…,Xn∼iidexp(λ). Let

λˆn:=n∑ni=1Xi

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

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

λ∈[λˆn−qα/2λn−−√,λˆn+qα/2λn−−√]=:I

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

Why is this the case?

Answer 1