  We study a system in which two-state Markov sources send status updates to a
common receiver over a slotted ALOHA random access channel. We characterize the
performance of the system in terms of state estimation entropy (SEE), which
measures the uncertainty at the receiver about the sources' state. Two channel
access strategies are considered: a reactive policy that depends on the source
behaviour and a random one that is independent of it. We prove that the
considered policies can be studied using two different hidden Markov models and
show through a density evolution analysis that the reactive strategy
outperforms the random one in terms of SEE while the opposite is true for age
of information. Furthermore, we characterize the probability of error in the
state estimation at the receiver, considering a maximum a posteriori and a
low-complexity (decode & hold) estimator. Our study provides useful insights on
the design trade-offs that emerge when different performance metrics are
adopted. Moreover, we show how the source statistics significantly impact the
system performance.
