A sequence \(X_1,…,X_n\) is draw iid from either \(\mbox{N}(0,1)\) or   \(\mbox{N}(0,10)\) with equal prior probability.

1. State the formulae for the probabilities that the sequence came from the normal with mean \(1\) or mean \(10\).
2. If you know the mean of the normal is \(1\) then what is the variance of \(S = \sum_i X_i\) and  \( \hat{\mu} = \frac{1}{n} \sum_i X_i\).
3. What is \(\mbox{Pr}(Z > \max\{x_1,…,x_n\})\) if \(\mu =1\) and \(\mu =10\).