f(x)=3/64x^2(4-x)
what is the moment generating function?
how do i find the mean and variance?
any help would really be appreciated since i dont understand anything concerning this
thankx
This is not right. The moment generating function is defined as
$\displaystyle M_X (t) = \mathbb{E}e^{Xt} = \int_{\mathbb{R}} e^{xt}f(x) dx$
(for continuous distributions). I would help with the computation but I can't figure out what the density is supposed to be from the OP.
I assume you mean $\displaystyle f(x) = \frac{3}{64} x^2 (4 - x)$. This pdf is incomplete as you do not include the interval over which this expression is defined (the support).
You should know that you need to calculate $\displaystyle E\left(e^{tX}\right) = \int e^{tx} \frac{3}{64} x^2 (4 - x) \, dx$ (and I have not included the integral terminals since you did not completely define the pdf). So please show all your working and clearly state where you are stuck.
Your mgf is OK: - Wolfram|Alpha
I assume at this level you can correctly differentiate and substitute t = 0. You can check your own answer using the definition of E(X): Calculate $\displaystyle 0.15 \int_{1/2}^{+\infty} x e^{-0.15(x - 0.5)} \, dx$.