👉 Residence math is a set of techniques in probability theory used to calculate the expected value of a random variable when its distribution is known only up to a fixed measure, typically the Lebesgue measure. It involves defining an upper and lower bound for the expected value by considering all possible realizations of the random variable within a specific set, often a measurable subset of the sample space. The key idea is to find these bounds by integrating over the set where the random variable takes on values within the specified range, effectively capturing all scenarios consistent with the given constraints. The expected value is then obtained by subtracting the lower bound from the upper bound, providing a precise estimate of the average outcome. This method is particularly useful when dealing with complex distributions or when exact probabilistic information is not available, offering a robust way to approximate expectations in various applications, from finance to physics.
