W9-slides1 - Lecture 25- Outline and Examples Expectation,...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 25- Outline and Examples Expectation, Covariance, Variance and Correlation (Ross § 7.4)
Background image of page 1

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

View Full DocumentRight Arrow Icon
Expectation Example. Sample mean. Let X 1 , X 2 , ··· , X n be independent and identically distributed (i.i.d.) random variables having common distribution function F and expected mean μ . Such a sequence of random variables is said to constitute a sample from the distribution F . The quantity ¯ X = n X i =1 X i n is called the sample mean . Compute E [ ¯ X ]. Solution.
Background image of page 2
Example. Sample mean. Let X 1 , X 2 , ··· , X n be independent and identically distributed (i.i.d.) random variables having common distribution function F and expected mean μ . Such a sequence of random variables is said to constitute a sample from the distribution F . The quantity ¯ X = n X i =1 X i n is called the sample mean . Compute E [ ¯ X ]. Solution. E [ ¯ X ] = E " n X i =1 X i n # = 1 n E " n X i =1 X i # = 1 n n X i =1 E [ X i ] = μ since E [ X i ] μ. The expected value of the sample mean is
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

W9-slides1 - Lecture 25- Outline and Examples Expectation,...

This preview shows document pages 1 - 4. Sign up to view the full document.

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