Cramér’s Theorem

Cramér’s Theorem is a fundamental result in probability theory that describes how the sums of many independent, identical random variables behave. Specifically, it states that the probability of the sum deviating significantly from its expected value decreases exponentially as the number of variables increases. This theorem helps quantify the likelihood of rare events in large samples, and is key in understanding large deviations from expected outcomes, providing a mathematical foundation for fields like risk assessment, statistical inference, and information theory.