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 $\displaystyle \mathbb{E}[f(X)]$?

Printable View

- May 11th 2009, 06:14 PMMMath09How 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 $\displaystyle \mathbb{E}[f(X)]$? - May 11th 2009, 08:50 PMCaptainBlack
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 - May 12th 2009, 03:08 PMMMath09
Hmmm... what if I also have the variance below the mean and the variance above the mean? Any better?

- May 12th 2009, 07:47 PMCaptainBlack