I have data of events in time. At the moment they are represented by (black) markers, at y = 1 on a scatter plot where the x-axis is time. Unfortunately there is uncertainty in x of about 2 hours. So I want to turn my black markers into more like grey sausage shapes - where there is an equal probability of the event occurring at each point in time in that 2 hours, and the shading is not black such that when all the events are plotted I can see the density building up at different points in time.
Any idea how I blur my precise markers over time into differentially-shaded uniform-probability sausages?
Thanks very much and let me know if this is not clearly stated as a question.