Epilepsy is a neurological condition such that it affects the brain and the nervous system. It is characterized by recurrent seizures, which are physical reactions to sudden, usually brief, excessive electrical discharges in a group of brain cells. Hence, seizure identification has great importance in clinical therapy of epileptic patients. Electroencephalogram (EEG) is one of the main biomarker that can measure voltage fluctuations of the brain and EEG data analysis helps to investigate the patient with epilepsy syndrome as epilepsy leaves their signature in EEG signals. In this paper, the Discrete Wavelet Transform (DWT) is applied to EEG signals to pre-processing, decompose it till the 4th level of decomposition tree.Various features like Entropy, Min, Max, Mean, Median, Standard deviation, Variance, Skewness, Energy and Relative Wave Energy (RWE) were computed in terms of detailed coefficients and the approximation coefficients of the last decomposition level.Then, the extracted features are evaluated by three modern machine-learning classifiers such as Radial Basis Function based Support Vector Machine (SVMRBF), k-Nearest Neighbor (KNN) and Naive Bayes (NB). The experimental results demonstrate that the highest classification accuracy (100\%) for normal subject data versus epileptic data is obtained by SVMRBF. the corresponding accuracy between normal subject data and epileptic data using KNN and NB is obtained as 99.50\% and 99\% for the eyes open and eyes closed conditions, respectively. The similar accuracies, while comparing the interictal and ictal data, are obtained as 99\%, 97.50\% and 98.50\% using the SVMRBF, KNN and NB classifiers, respectively. These accuracies are quite higher than earlier results published.