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This paper contributes a study on i-vector based speaker recognition systems and their application to forensics. The sensitivity of i-vector based speaker recognition is analyzed with respect to the effects of speech duration. This approach is motivated by the potentially limited speech available in a recording for a forensic case. In this context, the classification performance and calibration costs of the i-vector system are analyzed along with the role of normalization in the cosine kernel. Evaluated on the NIST SRE-2010 dataset, results highlight that normalization of the cosine kernel provided improved performance across all speech durations compared to the use of an unnormalized kernel. The normalized kernel was also found to play an important role in reducing miscalibration costs and providing well-calibrated likelihood ratios with limited speech duration.