Suppose a continuous random variable has a probability density function given by $f(x)=\frac{1}{x^2}$ for all $x > 1$ and $0$ otherwise.
This is a valid pdf since $\int_{-\infty}^{\infty}f(x)\,dx = 1$.
My question is, what is the mean and standard deviation of this distribution?
If I try to calculate
$$\mu=\int_{-\infty}^{\infty}xf(x)\,dx=\int_{1}^{\infty}\frac{1}{x}\,dx = \infty$$
The calculation of standard deviation requires the value of $E(X^2)$ which also similarly diverges. Am I doing this correct or is there something I'm missing?