- Let X1, X2, . . . , Xn be independent and identically distributed random variables with a common density function
f(x,θ) = e−(x−θ)I(x ≥ θ), where θ ∈ R.
- Find the maximum likelihood estimator θn of θ based on X1, . . . , Xn.
- Show that is consistent for .
- For a suitable normalizing factor (to be specified by you), find a non-degenerate limiting distribution of .