Epilepsy is one of the most common neurological disorders that greatly impair patients' daily lives. Traditional epileptic diagnosis relies on tedious visual screening by neurologists from lengthy EEG recording that requires the presence of seizure (ictal) activities. Nowadays, there are many systems helping the neurologists to quickly find interesting segments from the lengthy signal by automatic seizure detection. However, we notice that it is very difficult, if not impossible, to obtain long-term EEG data with seizure activities for epilepsy patients in areas lack of medical resources and trained neurologists. Therefore, we propose to study automated epileptic diagnosis using interictal EEG data that is much easier to collect than ictal data. The authors are not aware of any report on automated EEG diagnostic system that can accurately distinguish patients' interictal EEG from the EEG of normal people. The research presented in this paper, therefore, aims to develop an automated diagnostic system that can use interictal EEG data to diagnose whether the person is epileptic. Such a system should also detect seizure activities for further investigation by doctors and potential patient monitoring. To develop such a system, we extract three classes of features from the EEG data and build a Probabilistic Neural Network (PNN) fed with these features. Leave-one-out cross-validation (LOO-CV) on a widely used epileptic-normal data set reflects an impressive 99.3% accuracy of our system on distinguishing normal people's EEG from patients' interictal EEG. We also find our system can be used in patient monitoring (seizure detection) and seizure focus localization, with 96.7% and 76.5% accuracy respectively on the data set.