The question of how to validate and interpret correctly the waiting time probability density functions (WT-PDFs) from single molecule data is addressed. It is shown by simulation that when a stretched exponential WT-PDF, off ( t )= 0 e -( t / t ) α, generates the off periods of a two-state trajectory, a reliable recovery of the input off ( t ) from the trajectory is obtained even when the bin size used to define the trajectory, d t, is much larger than the parameter t. This holds true as long as the first moment of the WT-PDF is much larger than d t. Our results validate the results in an earlier study of the activity of single lipase B molecules and disprove recent related critique.