Unbiasedness for a Poisson sample

Let $X_1,X_2,…,X_n$ be a random sample of size $n$ ($\ge 2$) from a population having Poisson distribution with mean $\lambda$, where $\lambda > 0$ is an unknown parameter. If $T_1 = \bar{X}$ and $T_2 = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(X_i - \bar{X})^2}$, where $\bar{X} = \frac1n \sum_{i=1}^{n} X_i$, then which of the following statements is/are true?