  We consider linear systems subject to packet dropouts and obtain necessary
and sufficient conditions for an arbitrary state transfer and state estimation
over a finite time instance $T$. The data loss signal is modeled using the
Bernoulli random variable. We leverage properties of the Hadamard product in
our approach and use the derived necessary and sufficient conditions to compute
the probability that an arbitrary state transfer is possible at a specified
time instant. Similarly, the probability of finding an exact state estimate is
found using the observability counterparts of the results.
  Using the necessary and sufficient conditions obtained for the invertibility
of the Gramian, we give
  new probabilistic measures for optimal actuator and sensor placement problems
and obtain optimal/sub-optimal solutions.
  We demonstrate by an example how the probabilities of packet dropouts
influence the choice of an optimal actuator.
  We also discuss how to implement feedback laws and the LQR problem for these
models
  involving packet dropouts.
