Reference no: EM131852959

The elevator in a high-rise apartment is presumed to behave like a simple Markov process in the following sense. The elevator is observed each time it stops at or returns to the street floor. Its state on arrival is either empty, 0; partially full, 1; or full, 2. Consecutive observations of the elevator totaling 101 were made. Therefore, 100 transitions were observed. In 35 of them the car was initially empty; 5 of these were followed by full states, 15 by partially full states. In 45 of the transition observations the car was initially partially full; 20 were followed by an empty car and 20 by a partially full car. Of the 20 initially full cars, none was followed by an empty car, and 10 were followed by full cars. Use the obvious fractions to estimate the nine transition probabilities for this (homogeneous) Markov chain. Are these estimators independent random variables? Would estimators based on 100 nonconsecutive transition observations (e.g., observe one transition a day for 100 days) be "better" estimators (i.e., have smaller variance)? Would these nine estimators be independent?