Chapter 7 - Central Limit Theorem Flashcards
State Lemma 7.4 on linearity and sum of independant variable results for characteristic functions.
Define the characteristic function of a random variable.
How is it calculated for X with a continuous versus discrete distribution?
What is the characteristic function for X with normal distribution?
What is the characteristic function for X with normal distribution?
State Lemma 7.5 on expanding characteristic functions as a series.
State Theorem 7.6 - The Inversion Theorem. What does this reduce to if X has density function f(x)?
Do we need calculus Lemma 7.9?
State Theorem 7.7 - The Uniqueness Theorem.
State Theorem 7.8 - Levy’s Convergence Theorem.
Uniqueness: each characteristic function only corredponds to one distribution.
State Theorem 7.10 - The Central Limit Theorem.
