Predicting query execution time is a fundamental issue underlying many database management tasks. Existing predictors rely on information such as cardinality estimates and system performance constants that are difficult to know exactly. As a result, accurate prediction still remains elusive for many queries. However, existing predictors provide a single, point estimate of the true execution time, but fail to characterize the uncertainty in the prediction. In this paper, we take a first step towards providing uncertainty information along with query execution time predictions. We use the query optimizer's cost model to represent the query execution time as a function of the selectivities of operators in the query plan as well as the constants that describe the cost of CPU and I/O operations in the system. By treating these quantities as random variables rather than constants, we show that with low overhead we can infer the distribution of likely prediction errors. We further show that the estimated prediction errors by our proposed techniques are strongly correlated with the actual prediction errors.