When Pierce is on the phone with his mother, she states that she saw his father's ghost again, implying that Pierce's father is dead. Later, it is revealed that Pierce's father is indeed alive and appears in a subsequent season (only to die of a heart attack triggered by Jeff Winger).
About 10:27, Jeff first walks into the faculty party, one of the lights on the table is out, and stays out for the first couple of shots, after the medium wide shot, showing Jeff and the Prof, the light is re lit.
Professor Slater says that the Bernoulli distribution is the "number of successes in a sequence of independent yes/no experiments." She is describing the binomial distribution, not the Bernoulli distribution, which is a single yes/no experiment.