{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2 sx 1 n1 1 n1 1 n1 1 n1 n xi x 2 i 1 xi

Info icon This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: ounded by sx /t 2 . 2 sx = 1 n−1 = 1 n−1 ≥ 1 n−1 n ¯ (xi − x )2 i =1 ¯ (xi − x )2 + ¯ {i :|xi −x |>t } ¯ (xi − x )2 ¯ {i :|xi −x |>t } 1 n−1 ¯ (xi − x )2 ¯ {i :|xi −x |≤t } Chebechev’s inequality says ¯ The proportion of observations more than t from x is 2 bounded by sx /t 2 . 2 sx = 1 n−1 = 1 n−1 ≥ ≥ 1 n−1 1 n−1 n ¯ (xi − x )2 i =1 ¯ (xi − x )2 + ¯ {i :|xi −x |>t } ¯ (xi − x )2 ¯ {i :|xi −x |>t } t2 ¯ {i :|xi −x |>t } 1 n−1 ¯ (xi − x )2 ¯ {i :|xi −x |≤t } Chebechev’s inequality says ¯ The proportion of observations more than t from x is 2 bounded by sx /t 2 . 2 sx = 1 n−1 = 1 n−1 ≥ ≥ 1 n−1 1 n−1 n ¯ (xi − x )2 i =1 ¯ (xi − x )2 + ¯ {i :|xi −x |>t } ¯ (xi − x )2 ¯ {i :|xi −x |>t } t2 ¯ {i :|xi −x |>t } 1 ¯ ≥ t 2 #{i : |xi − x | > t } n 1 n−1 ¯ (xi − x )2 ¯ {i :|xi −x |≤t } Elements of Probability Theory With a li4le combinatorics Think about whether the “setup” comports with common sense We’ll draw some far- reaching conclusions, so you want to be sure that the foundaAons are solid. Sample Space •  All possible outcomes •  We wouldn’t have “probability” if there were only one possible outcome •  Even if we don’t know the sample space, there sAll “is” one Example of Sample Space •  Record the blood pressure of the next three people to be admi4ed to a blood pressure study. –  What do you think is the sample space? When the sample space is more than the possible outcomes. •  (Some of) the “random” factors that influence the sample space could be included as latent aspects of the outcome, and so contribute to a more complicated sample space. Events •  Subsets of the sampl...
View Full 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