lec23 - – mean variance • standard normal CDF Example...

This preview shows pages 1–8. Sign up to view the full content.

LECTURE 23 •Readings: Section 7.4, 7.5 Lecture outline • Proof of the central limit theorem • Approximating binomial distributions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
CLT Review i.i.d. finite variance variance standard normal (zero mean, unit variance) CLT : For every : Normal approximation: – Treat as if normal .
“Proof” of the CLT Assume for simplicity Need to show that converges to standard normal. We have: which is the transform of the standard normal.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Apply to Binomial • Fix , where : Bernoulli( ) : Binomial(

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) – mean , variance • standard normal CDF Example • ; find • • Exact answer: The ½ correction for binomial approximation • because is integer. • Compromise: consider De Moivre-Laplace CLT (for binomial) • When the ½ 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 •...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern