NotesSep15 - Example Let X,Y and Y be a continuous random...

Info iconThis preview shows pages 1–6. 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

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

View Full DocumentRight 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: Example: Let ( X,Y ) and Y be a continuous random vector, with a density f X,Y ( x,y ) = 15 xy 2 , < x,y < 1 , y ≤ x. Are X and Y independent? Functions of independent variables If X 1 ,X 2 ,...,X n are independent random vari- ables, then the random variables g 1 ( X 1 ) , g 2 ( X 2 ) ,... , g n ( X n ) are also independent. More generally, if we split independent random variables into disjoint groups, then functions of different groups are also independent. The Expected Value Recall that the expected value, or the expec- tation, or the mean of a random variable is the weighted average of its values, with the weights being the likelihoods of the values. Notation : E ( X ) or EX . Often also μ X or simply μ are used. For a discrete random variable X with a pmf p X the expected value is defined by EX = X a i a i p X ( a i ) . For a continuous random variable X with a pdf f X the expected value is defined by EX = Z ∞-∞ xf X ( x ) dx. Suppose X is a nonnegative random random variable. This means thatvariable....
View Full Document

This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell.

Page1 / 10

NotesSep15 - Example Let X,Y and Y be a continuous random...

This preview shows document pages 1 - 6. Sign up to view the full document.

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