We consider a stochastic scheduling problem with impatience to the end of service or impatience to the beginning of service. The impatience of a job can be seen as a stochastic due date. Processing times and due dates are random variables. Jobs are processed on a single machine with the objective to minimize the expected weighted number of tardy jobs in the class of static list scheduling policies. We derive optimal schedules when processing times and due dates follow di erent probability distributions.