Cramér's Theorem is a fundamental result in probability theory that provides a large deviation principle for sums of independent random variables. It essentially states that the probability of the sum deviating significantly from its expected value decreases exponentially with the distance from the mean, specifically illustrating how rare large deviations can be in probabilistic terms. This theorem connects deeply with concepts in limit theorems and large deviation principles, shedding light on the behavior of random variables and their cumulative distributions.
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