Carport Oil Drips

This is a stain on carport floor of my mother's home.  It comes from the the persistent drip of oil from her parked car and the variability of her parking location. When the car enters the carport from the bottom of this picture, the front of the car (and its motor) stops over the developing stain. The stain pattern running from the bottom to the top in the picture is from parking less or more of the car, respectively, in the carport. The left to right stain is from the car entering the carport more to the left or right.

Notice the prominent lines of oil drops on the right side of the stain. It could be from repetitive and quite accurate placement of the car more on the right of the carport. But it could also be a re-positioning of the car more forward or backward after it stopped on an established an entry line. This illustrates the conditional distribution of bottom to top oil placement given a fixed left to right car approach. Notice that it's likely that the floor is not level, indicated by the lighter, more liquid stain running towards the entry of the carport.

What results is a joint, two-dimensional scatterplot of automobile placement in the carport. The overall pattern of the oil is consistent with a targeted, ideal car placement. With a few other assumptions, such as independence of bottom to top and left to right placement, it is possible to prove that the resulting joint distribution is that of a bivariate normal distribution. More on the details in a future post.