Statistical Inference — MLE properties for a squared-exponential scale family

Let $x_1, x_2, x_3, …, x_n$ be a random sample from a distribution with probability density function $f(x; \theta) = \frac{2x}{\theta}e^{-\frac{x^2}{\theta}}$; $x > 0$, $\theta > 0$. Which of the following statements are correct in respect of parameter $\theta$ of the distribution? I. The maximum likelihood estimate of $\theta$ is given by $\hat\theta_{MLE} = \frac{1}{n}\sum_{i=1}^{n}x_i^2$. II. $\hat\theta_{MLE}$ is an unbiased estimator of $\theta$. III. $\hat\theta_{MLE}$ is sufficient estimator of $\theta$. Select the answer using the code given below.