Electrical activity of human brain changes with the human reactions to the situations, thoughts processing and with different mental states of mind. Brain Computer Interface uses different features of brain electrical activity to create a parallel communication pathway and replaces traditional pathway of nervous system to control numerous applications, by the patients suffering from severe motor disorders. Formation of a Brain Computer Interface is carried out in steps which include preprocessing, feature extraction and classification of Electroencephalogram signals to generate a meaningful command. As Electroencephalogram signals change with different alertness level of human brain, this can cause a false interpretation of Electroencephalogram signals as a patient's alertness may change severely due to medicines with high alcoholic content. A methodology is proposed in present work for feature extraction and classification of Electroencephalogram signals recorded from drowsy and controlled subject. The raw Electroencephalogram data is filtered to extract μ and β wavebands using Butterworth filter. Discrete wavelet coefficients are calculated from filtered data and further processed by Principal Component Analysis for dimensionality reduction. Statistical parameters calculated as features from reduced data set, are used to prepare the input feature vector to train the classifier. Support Vector Machine classifier classifies the two classes of data.