Refer to the sleep apnea study published below. Recall that the various stages of sleep for a large group of sleep apnea patients were monitored in 30-second "epochs", and the sleep stage for the previous and current epoch was determined.
a). Given that the previous sleep stage for the epoch was the Wake state, what is the
b). Given that the current sleep for the epoch is REM, what is the probability that the previous sleep stage was not the wake state?
c). Are the
d) Are the events (previous stage is REM) and (current stage is REM) independent?
3). Are the events (previous stage is Wake) and (current stage is Wake) independent?