notes-09-01

notes-09-01 - M4056 Lecture Notes. September 1, 2010...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: M4056 Lecture Notes. September 1, 2010 Section 5.2. (cont.) Reminders: i ) E ( aX + bY ) = a E ( X ) + b E ( Y ) ii ) E ( X 2 ) = Var ( X ) + E ( X ) 2 (see page 60, 2.3.1) iii ) Var ( aX + b ) = a 2 Var ( X ) (see page 60) iv ) If X and Y are independent, Var ( aX + bY ) = a 2 Var ( X ) + b 2 Var ( Y ). (Word to wise: good material for quiz questions here.) Suppose X 1 , . . ., X n iid . Suppose is the expected value of the common distribution of the X i and 2 is its variance. The two statistics of greatest importance are: The sample mean: X := 1 n n i =1 X i , The sample variance: S 2 = 1 n- 1 n i =1 ( X i- X ) 2 . The expected value and variance of the statistic X . E ( X ) = 1 n ( E ( X 1 ) + + E ( X n )) = (Theorem 5.2.6.a, p. 213-4). V ar ( X ) = 1 n 2 ( V ar ( X 1 ) + + V ar ( X n )) = 2 /n (Theorem 5.2.6.b, p. 213-4). To deduce information about S 2 (see next page), we will use a fact of arithmetic: Theorem 5.2.4. For any numbers...
View Full Document

Page1 / 2

notes-09-01 - M4056 Lecture Notes. September 1, 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online