Let Y1 and Y2 denote the proportions of two different types of components in a sample from a mixture of chemicals used as an insecticide. Suppose that Y1 and Y2 have a joint density function given by:

f(y1,y2) = {2, 0 <= y1 <= 1, 0 <= y2 <= 1, 0 <= y1 + y2 <= 1,

0, elsewhere.

Find P(Y1 <= 3/4, Y2 <= 3/4)

Here was my approach:

I took the double integral of 2 evaluated from 0 to 3/4 with respect to y1 and then y2. I got 3/4 as my answer and think I'm doing something wrong. How would you go about this? Thanks!!