Looking at a problem where X is lognormally distributed from normal distribution Y, which asks me to prove that:
1) $e^{\bar{y}}$ is a biased estimator for the median of X
2) $e^{\bar{y} - \sigma^2 / (2n)}$ is an unbiased estimator for the median of X
3) $e^{\bar{y} - \sigma^2 / (2n)}e^{\sigma^2/2}$ is an unbiased estimator for $\mu_x$
I know that I'm being asked to solve for $E(\hat\theta) = \theta$, but I'm absolutely adrift as to how to actually calculate the expected value of the estimators. If someone could cluebat me, I would be appreciative.