lec23 - ) mean , variance standard normal CDF Example ;...

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LECTURE 23 • Readings: Section 7.4, 7.5 Lecture outline • Proof of the central limit theorem • Approximating binomial distributions
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CLT Review i.i.d. finite variance variance standard normal (zero mean, unit variance) CLT : For every : • Normal approximation: – Treat as if normal .
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“Proof” of the CLT • Assume for simplicity • Need to show that converges to standard normal. •We have
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Apply to Binomial •F ix , whe re : Bernoulli(
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Unformatted text preview: ) mean , variance standard normal CDF Example ; find Exact answer: The correction for binomial approximation because is integer. Compromise: consider De Moivre-Laplace CLT (for binomial) When the correction is used, CLT can also approximate the binomial PMF (not just the CDF). Exact answer: Poisson vs. normal approximations of the binomial Binomial ( ) fixed, : normal fixed, : Poisson Poisson normal...
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This note was uploaded on 12/08/2010 for the course MATH 6.041 / 6. taught by Professor Muntherdahleh during the Spring '10 term at MIT.

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lec23 - ) mean , variance standard normal CDF Example ;...

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