Consistent estimator for parameter from Rayleigh distribution.

[pirce]

Welcome

Using MLE I found that estimator $$\alpha$$ parametr from Rayleigh distribution is described by formula
$$\hat{\alpha}=\sqrt{\frac{\sum_{n}^{i=1}x_i^2}{2n}}$$
but I can't proof that this estimator is consistent estimator.

Would you be mind and help me with my problem.

 

[bpet]

Wouldn't you just need to show that E[X^2] = 2a^2 ?