  We compare two statistical models of three binary random variables. One is a
mixture model and the other is a product of mixtures model called a restricted
Boltzmann machine. Although the two models we study look different from their
parametrizations, we show that they represent the same set of distributions on
the interior of the probability simplex, and are equal up to closure. We give a
semi-algebraic description of the model in terms of six binomial inequalities
and obtain closed form expressions for the maximum likelihood estimates. We
briefly discuss extensions to larger models.
