I am given the following probability density function:
for 0<x<1 and 0<y<2
otherwise
I am to find P[X + Y > 1].
My attempts at the double integration failed.
The answer begins:
How did they pick which integral was inner?
How did they choose 1-x as the lower limit on the inner integral?
Draw the line x + y = 1 inside the rectangle defined by 0 < x < 1 and 0 < y < 2. This line divides the rectangle into two regions: The region above the line (upper region) and the region below the line (lower region). Note that in the upper region x + y > 1. So you need to set up a double integral of f(x, y) over the upper region .......