The weak law, also known as the weak law of large numbers, states that the sample average of a sequence of independent and identically distributed random variables converges in probability to the expected value as the sample size increases. This means that for any small positive number, the probability that the sample average deviates from the expected value by more than that number approaches zero as the number of observations goes to infinity. It provides a foundational understanding of how averages behave under repetition, which is crucial for statistical inference.
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