Q:

Infinite Expected Value of Jointly Distributed Random Variables

I am given a joint pdf function $f(x,y)$ of random variables $X$ and $Y$ such that
$f(x,y) = cxy^{-2}$ when $0 < x < 1$, $1 < y$
$f(x,y) = 0$ otherwise
where $c$ is a constant. 
I have calculated the value of $c$, and computed the marginal pdf's of $X$ and $Y $ -- which, from my computations, appear to be independent -- but am having trouble understanding how to calculate the expected value for $Y$.
By integrating $f(x,y)$ over the domain $(0,1)$ with respect to $x$, I computed
$f_{Y}(y) = y^{-2}$
Now, the problem asks to compute $E[Y]$, which led me to try to compute 
$\int\limits_1^\infty y(y^{-2})dy$, giving me the result $E[Y] = \lim_{y \to \infty} \ln(y)$.
Intuitively, this doesn't make sense to me. Am I doing something wrong? If not, what does it mean for the expected value of a random variable to be infinite?

A:

You're quite correct: the integral diverges, and $E[Y]$ does not exist: we can say $E[Y] = +\infty$ in this case, because it diverges to $+\infty$.  

