probability theory - how to find an actual number for E(X) with the given information?

Let $X$ be a positive continuous random variable with the probability density function $f_X(t)$. Suppose that there is a random variable $Y$, for which the pdf is $f_Y(t) = t\,f_X(t)$ (for all real numbers $t$). What is $E(X)$ (find an actual number)? Express $\operatorname{var}(X)$ in terms of $E(Y)$.