I want to define a mathematical model (formula) to design missing information from sampling. In my problem, I have real events whose value is binary (0, 1) which might change every second. For a given sample period, $p$, I periodically checks the value at $t$, and assumes the value stays the same until the next observation time, $t+p$. Obviously, there must be missing information proportional to the sampling period. Is there a mathematical formula (model) to express the missing information rate?
In the above figure, the top part is the real events, and the below part is the constructed events from the sampling. The sampling rate is two, and it is missing the real value from time between 1 and 2, 3 and 4, 5 and 6.
Can someone please give me advice how to model it?
Thanks in advance.