$X$ is a random variable with a scaled t distribution with $d=5$. Density: $$f(x)=\frac{\Gamma(\frac{d+1}{2})}{\theta\sqrt{d\pi}\Gamma(d/2)} ( 1+\frac{x^2}{d\theta ^2})^{-\frac{d+1}{2}}$$
How do I prove that the unbiased estimate of $\theta^2$ is given by $$\hat{\theta^2}=\frac{3}{500}\sum^{100}_{i=1}x^2_i,$$ where we have a sample size of 100 generated data points when $\theta=2$. How do I Use this formula to estimate $\theta$? I assume taking the square root?
I need to prove the estimator is unbiased, any help is greatly appreciated :)