Support vector machines (SVMs), and kernel classifiers in general, rely on the kernel functions to measure the pairwise similarity between inputs. This paper advocates the use of discrete representation of speech signals in terms of the probabilities of discrete events as feature for speaker verification and proposes the use of Bhattacharyya coefficient as the similarity measure for this type of inputs to SVM. We analyze the effectiveness of the Bhattacharyya measure from the perspective of feature normalization and distribution warping in the SVM feature space. Experiments conducted on the NIST 2006 speaker verification task indicate that the Bhattacharyya measure outperforms the Fisher kernel, term frequency log-likelihood ratio (TFLLR) scaling, and rank normalization reported earlier in literature. Moreover, the Bhattacharyya measure is computed using a data-independent square-root operation instead of data-driven normalization, which simplifies the implementation. The effectiveness of the Bhattacharyya measure becomes more apparent when channel compensation is applied at the model and score levels. The performance of the proposed method is close to that of the popular GMM supervector with a small margin.