A question as to whether a human being is aware they are dead once they die also elicits equally, hard to answer response.
According to science, as a human being pass on, his or her brain activities come to a halt. This includes the part of the brain that has functions of being conscious and having an awareness. Therefore, from the strictly biological viewpoint, it may be assumed that a person would not be aware of his or her own dying.
But there are some sort of stories of near-death, when people say they feel themselves conscious and active, while their bodies are no more alive, according to doctors. Such encodings are typically characterised as calm and deep. It is however important to appreciate the fact that these accounts are personal and cannot be scientifically validated.
Lastly, as to the question of whether a person knows he or she is dead after death, this remains a critical philosophical and Spritual issue that can be linked to the culture and experience of a given individual.