Characteristic Functions and the Central Limit Theorem
The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.37) and for independent arrays of random variables (Lindeberg-Feller theorem, Theorem 15.43). For the latter, we prove only that one of the two implications (Lindeberg’s theorem) that is of interest in the applications.
KeywordsProbability Measure Characteristic Function Central Limit Theorem Probability Generate Function Nonnegative Random Variable
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