Results 1 to 3 of 3

Math Help - expectation proving question

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    2

    expectation proving question

    Prove that E[(Z - Uz)^2] = c^2(E[X^2] - (Ux)^2) if X is a discrete random variable and b and c are constants and define a new random variable Z = b + cX

    Note : Uz = mu of z = mean of z

    Ux = mu of x = mean of x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2009
    Posts
    2

    this is what i get upto....

    E ((Z-Uz)^2) = E(Z^2) - Uz^2 --- Eq1

    Uz = cUx

    subbing in z = b + cX in Eq1

    =E(b^2 + 2cX + (cX)^2) - (cUx)^2
    = b^2 + 2c *(E(X)) + c^2(E(X^2)) - c^2 * Ux^2
    = b^2 + 2cE(X) + c^2((E(X^2)) - Ux^2)

    Why do i get b^2 + 2cE(X) extra???????
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jus_a_kid View Post
    Prove that E[(Z - Uz)^2] = c^2(E[X^2] - (Ux)^2) if X is a discrete random variable and b and c are constants and define a new random variable Z = b + cX

    Note : Uz = mu of z = mean of z

    Ux = mu of x = mean of x
    By definition: E[(Z - \overline{z})^2] = Var[Z].

    And Var[Z] = Var[b + cX] = c^2 Var[X].

    And by definition Var[X] = E[X^2] - \overline{x}^2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Net profit Expectation Question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 9th 2011, 03:20 AM
  2. Basic expectation question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 22nd 2010, 08:42 PM
  3. need help with an expectation question
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 10th 2009, 05:11 PM
  4. Expectation Question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 5th 2009, 12:07 PM
  5. expectation question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 25th 2008, 07:10 AM

Search Tags


/mathhelpforum @mathhelpforum