Prove $\lambda_n$ is a biased estimator

Question

Let X be Random Variable with Exp($\lambda$), $\lambda>0$. Let $\hat{\lambda}_n = \frac{1}{\bar{X}_n}$, where $\bar{X}_n$ is sample mean. May I ask how to prove $\hat{\lambda}_n$ is a biased estimator for $\lambda$ ? I tried to start with $E[\hat{\lambda}_n] = E[\frac{1}{\frac{1}{n}\Sigma_{i=1}^{n} X}]$ but I could not get anything

Answer 1

Hint: Apply Jensen's equality to the expectation of $\hat{\lambda}_n$.