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Key applications in high-rate serial data technologies assume that random jitter follows a Gaussian distribution and require that receivers be tested under the stress of a calibrated level of Gaussian random jitter. However, the most commonly available noise sources have never been rigorously characterized until now. We perform a complete statistical analysis of industry-standard noise sources and report on the extent to which the Gaussian assumption is valid. By including both statistical and systematic errors in a complete chi-squared covariance analysis, we show how to calculate the "goodness-of-fit" confidence level without resorting to the commonly used but inadequate least-squares approach.