Results 1 to 4 of 4

Math Help - I have problems of understanding two statistical concepts

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    56

    I have problems of understanding two statistical concepts

    The followings are the definitions of Law of Iterated Expectations and Covariance from textbook.

    Law of Iterated Expectations:

    E[y] = Ex [E [y | x]]

    The notation Ex [.] indicates the expectation over the values of x. Note that E [y | x] is a function of x.

    Covariance:

    In any bivariate distribution,

    Cov [x, y] = Covx [x, E[y | x]] = Integration (x - E[x]) E[y | x] fx (x)dx

    (Note that this is the covariance of x and a function of x).


    Can people explain this two theories in plain words?

    What is the meaning of "the expectation over the value of x"?

    What does the textbook mean by "this is the covariance of x and a function of (x)"? Why is the textbook saying the equation Cov [x, y] is the covriance of x and a function of x?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Real9999 View Post
    The followings are the definitions of Law of Iterated Expectations and Covariance from textbook.

    Law of Iterated Expectations:

    E[y] = Ex [E [y | x]]

    The notation Ex [.] indicates the expectation over the values of x. Note that E [y | x] is a function of x.
    First we need Bayes' theorem:

    p(x,y)=p(x|y)p(y)=p(y|x)p(x)

    Then

    \displaystyle E(y)= \int_x \int_y y p(x,y)\;dydx

    and:

    \displaystyle E_x(E(y|x))=\int_x \left(\int_y y p(y|x)\;dy \right) p(x)\;dx

    .............. \displaystyle =\int_x \int_y \left( y \frac{p(x|y)p(y)}{p(x)} \right) p(x)\;dy dx= \int_x \int_y y p(x,y)\;dydx

    etc.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Real9999 View Post

    Covariance:

    In any bivariate distribution,

    Cov [x, y] = Covx [x, E[y | x]] = Integration (x - E[x]) E[y | x] fx (x)dx

    (Note that this is the covariance of x and a function of x).


    Can people explain this two theories in plain words?

    What is the meaning of "the expectation over the value of x"?

    What does the textbook mean by "this is the covariance of x and a function of (x)"? Why is the textbook saying the equation Cov [x, y] is the covriance of x and a function of x?
    Like the other just write out the definitions and apply Bayes' theorem and some algebra.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2010
    Posts
    56
    Thank you so so so much XD
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 8th 2010, 09:29 PM
  2. Replies: 0
    Last Post: November 10th 2009, 10:25 AM
  3. Help Understanding Math Concepts [URGENT]
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 10th 2009, 11:55 PM
  4. Help understanding these concepts
    Posted in the Algebra Forum
    Replies: 6
    Last Post: July 31st 2008, 08:42 AM
  5. Replies: 3
    Last Post: July 1st 2008, 05:29 PM

Search Tags


/mathhelpforum @mathhelpforum