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

Info iconThis 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

Ask a homework question - tutors are online