Find the Maximum Likelihood Estimator (MLE) of the parameter θ. Is the estimator

1. Let X1, ..., Xn be independent N(θ, θ^2) random variables where θ > 0 is a parameter.

Find the Maximum Likelihood Estimator (MLE) of the parameter θ. Is the estimator of θ: a) unbiased? b) efficient? c) sufficient? d) consistent? Justify your answers.
Include the definitions and theorems that you use in your answers.

When working through this problem we had an issue with finding a MLE that didn't involve an imaginary number.