Results 1 to 4 of 4

Thread: How do I find the mean of this?

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    9

    How do I find the mean of this?

    I have $\displaystyle \mathbb{E}[X]=\mu$

    $\displaystyle
    f(x) = \left\{
    \begin{array}{lr}
    2x^2 + x, & x \leq \mu\\
    x^2 + 3x + 1, & x \geq \mu
    \end{array}
    \right.
    $

    How do I find $\displaystyle \mathbb{E}[f(X)]$?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by MMath09 View Post
    I have $\displaystyle \mathbb{E}[X]=\mu$

    $\displaystyle
    f(x) = \left\{
    \begin{array}{lr}
    2x^2 + x, & x \leq \mu\\
    x^2 + 3x + 1, & x \geq \mu
    \end{array}
    \right.
    $

    How do I find $\displaystyle \mathbb{E}[f(X)]$?
    You don't have enough information to do any thing but write the expectation as an integral:

    $\displaystyle
    E(f(X))=\int_{-\infty}^{\infty} f(x) p(x)~dx=\int_{-\infty}^{\mu}(2x^2 + x) p(x)~dx +
    \int_{\mu}^{\infty}(x^2 + 3x + 1) p(x)~dx
    $

    where $\displaystyle p(x)$ the density of $\displaystyle X$.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2009
    Posts
    9
    Hmmm... what if I also have the variance below the mean and the variance above the mean? Any better?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by MMath09 View Post
    Hmmm... what if I also have the variance below the mean and the variance above the mean? Any better?
    Depending on what exactly you mean by those may-be.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: Mar 22nd 2011, 04:57 PM
  2. Replies: 2
    Last Post: Jul 5th 2010, 08:48 PM
  3. Replies: 1
    Last Post: Feb 17th 2010, 03:58 PM
  4. Replies: 0
    Last Post: Jun 16th 2009, 12:43 PM
  5. Replies: 2
    Last Post: Apr 6th 2009, 08:57 PM

/mathhelpforum @mathhelpforum