Lecture 10: Characteristic Functions
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چکیده
1.1 Complex random variables 1.2 Definition and basic properties of characteristic functions 1.3 Examples 1.4 Inversion formulas 2. Applications 2.1 Characteristic function for sum of independent random variables 2.2 Characteristic functions and moments of random variables 2.3 Continuity theorem 2.4 Weak law of large numbers 2.5 Central Limit theorem 2.6 Law of small numbers 1. Definition of characteristic function 1.1 Complex random variables (1) Complex numbers has a form u = a + ib where a, b are real numbers and i is so-called imaginary unit which has a property i 2 = −1.
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