Results 1 to 5 of 5

Math Help - [SOLVED] expected value

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    6

    [SOLVED] expected value

    Here is my problem:

    Find the expected value of g(X) = X^2 - 5X + 3, if the probability density is given by:
    f(x) = { \frac{x}{2} for 0<x<1
     <br />
\frac{1}{2} for 1<x<2
     <br />
\frac{3-x}{2} for 2<x<3
    0 elsewhere

    Can anyone help???
    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 penguin11 View Post
    Here is my problem:

    Find the expected value of g(X) = X^2 - 5X + 3, if the probability density is given by:
    f(x) = { \frac{x}{2} for 0<x<1
     <br />
\frac{1}{2} for 1<x<2
     <br />
\frac{3-x}{2} for 2<x<3
    0 elsewhere

    Can anyone help???
    E(g(x))=\int_{-\infty}^{\infty} g(x) f(x)~dx

    ........... =\int_0^1 g(x) \frac{x}{2} ~dx + \int_1^2 g(x) \frac{1}{2}~dx + \int_2^3 g(x) \left( \frac{3-x}{2}\right)~dx

    and these are all elementary integrals.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    6
    Ok, when I evaluate the integrals, I get E(g(x)) = -\frac{21}{4}. Does that look right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by penguin11 View Post
    Ok, when I evaluate the integrals, I get E(g(x)) = -\frac{21}{4}. Does that look right?

    No, numerically I get 1.8333, and when I do this exactly I get -22/12.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2008
    Posts
    6
    Thanks! I found my mistake. I really appreciate the help.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Moments and Expected Values using estimators.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 1st 2010, 03:22 PM
  2. [SOLVED] expected value
    Posted in the Statistics Forum
    Replies: 3
    Last Post: April 22nd 2009, 01:29 PM
  3. [SOLVED] Expected value of f(x,y) - Simple question
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 14th 2009, 11:39 PM
  4. Replies: 1
    Last Post: March 7th 2009, 10:22 AM
  5. [SOLVED] expected value of marbles
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 1st 2008, 10:59 AM

Search Tags


/mathhelpforum @mathhelpforum