I have an object that moves randomly back and forth across a line (L) with frequency of movement (F) and speed (S) dependent on temperature (T), and temperature raising at a rate(r). I would like to know whether the object is staying within a tract (tr=L/10; i.e. a tenth part of the line's length) during more time than expected by the length of the tract and speed of the object given its temperature. Is this possible?
If speed is length/time, I think it could be put in terms of the experiment's line, tract length with respect to line`s length, and of the rate of temperature rise. Then, extract the expected t for the given length of the tract, at any given temperature. That should allow to identify a maximum time spent per line's tract that can be expected by chance. However, I lack the skills to do that math reliably. I can offer coauthorship on an article in exchange for this help.
Thanks in advance!