The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount $Y$ from which a random amount $X$ is sold during that day. Assume that the joint density function of these variables is given by
$$f(x, y)=\left\{\begin{array}{ll}2, & 0<x<y, 0<y<1, \\0, & \text { elsewhere. }\end{array}\right.$$
Find the probability density function for the amount of kerosene left in the tank at the end of the day.