A soft-drink machine has a random amount Y₂ in supply at the beginning of a given day and dispenses a random amount Y₁ during the day (with measurements in gallons). It is not resupplied during the day, thus Y₁ ≤ Y₂. It has been observed that Y₁,Y₂ have a joint density function given by

f(y1, y2)= {1/2, 0≤ y1 ≤ y2 ≤ 2 }
{0, elsewhere. }

Find the conditional density of Y₁ given Y₂ = y₂.