Assume that for $i = 1,2,3,\dots,n$ we have $X_i \sim \mathcal{N}(\mu_i, 1)$ and assume that we know many of $\mu_i$s are zero.
How can we estimate the maximum of $\mu_i$s with a sample of $x_1,x_2,...,x_n$ such that each $x_i$ is modelled by $X_i$
Can we use maximum likelihood? Or the Bayes rule?