Determine the mean and variance of the sampe mean $\bar X = \dfrac{\sum_{i=1}^{5}X_i}{5}$ where $X_1,..X_5$ is random sample from a distribtuion having pdf $f(x)=4x^3$, $0<x<1$, zero elsewhere.
It's an unsolved problem from my exercise with no answer and solution. So i just wanted to know if i did solve it in right manner. Correct me if i did wrong. My results after solving are:
$E(\bar X)=\dfrac{4}{5}$
$E(\bar X^{2})=\dfrac{4}{6}$
$V(\bar X)=\dfrac{4}{6}-\dfrac{16}{25}=\dfrac{2}{75}$