Outliers

Suppose you have two observations, $y_1 =70$ and $y_2 = 100$, where $y_i = \mu + \epsilon$ with which to estimate the value of $\mu$, with $\epsilon_1 \tilde N(0,10)$ and $\epsilon_2\tilde \{(.5, -40), (.5, +40)\}$. What should our estimate $\hat{\mu}$ be?

This would make a good note. American Mathematical Monthly. Get a loss function-- probably any convex loss function is OK, but start with quadratic. The answer must be something like 104. The point is: don't discard outliers, but think about what htey mean.

I need to get the Math extension to work in Mediawiki. I have it in localsettings, so i just need it to update. 

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