Lecture 5 (7).pdf - IEMS 303 Lecture 5 0.1 To Do • Read Chapter 6.1–6.2 • Submit Lab 3(Due –11:59pm–CANVAS • Start Homework 3(Due

Lecture 5 (7).pdf - IEMS 303 Lecture 5 0.1 To Do • Read...

This preview shows page 1 - 2 out of 7 pages.

IEMS 303 Lecture 5 0.1 To Do... • Read Chapter 6.1–6.2 • Submit Lab 3 (Due 10/09/2019–11:59pm–CANVAS) • Start Homework 3 (Due 10/15/2019–2:00pm–w/o R parts in class, w/ R parts on CANVAS) 0.2 Learning Goals • Overview fitting a probability distribution • Describe histograms • Define moments of probability distributions • Uses the method of moments to fit a probability distribution 0.3 A note on sample standard deviatrion Given that x 1 , . . . , x n are independent and identically distributed with some mean and some variance σ 2 , then s 2 = 1 n 1 n i =1 ( x i ¯ x ) is unbiased estimator of σ 2 . Note that begin able to do a quick derivation of this is NOT critical to the course! Let y i = x i µ E ( s 2 ) = E 1 n 1 n summationdisplay i =1 ( x i ¯ x ) 2 . E ( s 2 ) = E 1 n 1 n summationdisplay i =1 ( x i µ ( ¯ x µ )) 2 . = E 1 n 1 n summationdisplay i =1 y i 1 n n summationdisplay i =1 y i 2 = 1 n 1 E n summationdisplay i =1 y i 2 2 n n summationdisplay i =1 n summationdisplay j =1 y i y j + n n 2 n summationdisplay i =1 n summationdisplay j =1 y i y j = 1 n 1 parenleftbigg n σ 2 parenrightbigg 2 n parenleftbigg n σ 2 parenrightbigg + 1 n parenleftbigg n σ 2 parenrightbigg = n 2 + 1 n 1 σ 2 = σ 2 This is why we divide by n 1 : it is an unbaised estimate. 1 Estimating a distribution 1.1 Overview Sometimes, instead of being curious about a particular property of a population (i.e. the population mean ), we are curious about the entire population distribution . To do this, we take our observed data and come up with an approximate population distribution . This process is commonly referred to as fitting a statistical model. We will call this the fitted distribution .
Image of page 1

Subscribe to view the full document.

Image of page 2
  • Summer '19
  • Mr. Bee

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

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes