  We give the distribution of $M_n$, the maximum of a sequence of $n$
observations from a moving average of order 1. Solutions are first given in
terms of repeated integrals and then for the case where the underlying
independent random variables are discrete. When the correlation is positive, $$
P(M_n \max^n_{i=1} X_i \leq x) = \sum_{j=1}^\infty \beta_{jx} \nu_{jx}^{n}
\approx B_{x} r{1x}^{n} $$ where $\{\nu_{jx}\}$ are the eigenvalues of a
certain matrix, $r_{1x}$ is the maximum magnitude of the eigenvalues, and $I$
depends on the number of possible values of the underlying random variables.
The eigenvalues do not depend on $x$ only on its range.
