class02-2-handouts

class02-2-handouts - PSTAT 120B Probability Statistics...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
PSTAT 120B - Probability & Statistics Class # 02-2- Central limit theorem Jarad Niemi University of California, Santa Barbara 7 April 2010 Jarad Niemi (UCSB) Central limit theorem 7 April 2010 1 / 19
Image of page 1

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

View Full Document Right Arrow Icon
Class overview Announcements Announcements Homework 1 is returned in class, come up afterwards to get yours A minimal solution guide will be made available Complete your answers, e.g. if the mgf is e ( λ 1 + λ 2 )( e t - 1) then the random variable is a Poisson with mean λ 1 + λ 2 . I still haven’t made corrections to Monday’s slides, but I plan to Society of actuaries Open House (next slide) Jarad Niemi (UCSB) Central limit theorem 7 April 2010 2 / 19
Image of page 2
Class overview Announcements Society of actuaries - open house Then you should consider a career as an actuary. Join us to learn more about one of today’s best careers. WHAT: Informational presentation and open house All interested students are welcome DINNER WILL BE PROVIDED. WHEN: Monday, April 12, 2010 4-6 p.m. WHERE: HSSB 1174 Please RSVP at: [email protected] For more information, contact [email protected] or visit www.RiskisOpportunity.net Jarad Niemi (UCSB) Central limit theorem 7 April 2010 3 / 19
Image of page 3

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

View Full Document Right Arrow Icon
Class overview Day’s Goals Goals Central limit theorems For averages For sums Beta distribution Continuity correction Jarad Niemi (UCSB) Central limit theorem 7 April 2010 4 / 19
Image of page 4
Central limit theorem Proportion Suppose Y 1 , Y 2 , . . . , Y n iid Ber(0 . 5). What is the distribution for Y n = 1 n n i =1 Y i ? n = 5 Y p ( Y 29 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 n = 15 Y p ( Y 29 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 n = 25 Y p ( Y 29 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 Jarad Niemi (UCSB) Central limit theorem 7 April 2010 5 / 19
Image of page 5

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

View Full Document Right Arrow Icon
Central limit theorem CLT Central Limit Theorem Let Y 1 , Y 2 , . . . , Y n be independent and identically distribution random variables with E ( Y i ) = μ and V ( Y i ) = σ 2 <
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern