simple scenarios X&Y might be independent meaning of the probability of x and y taking on specific value small X small Y is a probability of X taking on value x and y taking on value of y that's the case actually knowing X does not tell you anything about Y or the other way around so it's actually not so interesting case mathematically simplifies things but yeah if you had a sensor where your sensor is independent of the state of your system the sensor cannot inform you about the system sometimes the property that holds true