[Probability]need help to understand the following expression So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively. assume c is a constant. I am having huge trouble to understand the integration of the following expression. $P(Y<c/u(X))$ $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$ where t is the cross-point that $u(x)$ change sign * * * here $c/u(x)$ is given by the plot below, t is the point crossing the zero: !enter image description here **Confusion:** _I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot._

Actually, one is not interested in $P(Y
Note finally that $$P(Y