  We establish the capacity region of several classes of broadcast channels
with random state in which the channel to each user is selected from two
possible channel state components and the state is known only at the receivers.
When the channel components are deterministic, we show that the capacity region
is achieved via Marton coding. This channel model does not belong to any class
of broadcast channels for which the capacity region was previously known and is
useful in studying wireless communication channels when the fading state is
known only at the receivers. We then establish the capacity region when the
channel components are ordered, e.g., degraded. In particular we show that the
capacity region for the broadcast channel with degraded Gaussian vector channel
components is attained via Gaussian input distribution. Finally, we extend the
results on ordered channels to two broadcast channel examples with more than
two channel components, but show that these extensions do not hold in general.
