Random variables $X_1,...X_n$ are independent and identically distributed with $X_1$ having the probability density function:
$$ f(x;\theta) = 3\theta^3 \frac{1}{x^4} \space for \space x>0 $$
Where $\theta>0$ Is an unknown parameter.
Then :
$$E[X_1]= 3\theta^3 \int_\theta^\infty x x^{-4} dx $$
Why is the lower boundry of the integral $\theta$ and not $0$?
The definition of $f(x)$ should be for $x>\theta$ because $\int_{\theta}^{\infty}f(x)dx=1$.