Bias and consistency of the sample minimum

Let $X_1,…,X_n$ be a random sample from a population with the probability density function

$$f(x|\theta)=\begin{cases}4e^{-4(x-\theta)}, & x>\theta,\ 0, & \text{otherwise,}\end{cases}\quad\theta\in\mathbb R.$$

If $T_n=\min\{X_1,…,X_n\}$, then