Limit Theorems Week 8
A Couple of Inequalities T wo important... The Central Limit Theorem Central limit theorems are a set of weak convergence results in probability theory. Intuitively, they all express the fact that any sum of many small independent random variables is approximately normally distributed. These results explain the ubiquity of the normal distribution. The most important and famous result is simply called The Central Limit Theorem; it is concerned with independent variables with identical distribution whose expected value and variance are finite. Several generalizations exist which do not require identical distribution but incorporate some condition which guarantees that none of the variables exert a much larger influence than the others. Two such conditions are the Lindeberg condition and the Lyapunov condition. Other generalizations even allow some "weak" dependence of the random variables. The Law of Large Numbers Sampling Distributions Reference
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