Hello,

I'm trying to solve this problem:

If X and Y are independent and f(x) = 1/2 when 0<X<2 and f(y) = 2Y when 0<Y<1, find P(X<2Y).

My attempt:

As X and Y are independent, f(x,y) = Y when 0<X<2 and 0<Y<1.

I integrated Y first with respect to X from 0 to 2Y, then I integrated this with respect to Y from 0 to 1, which gives 2/3 for the answer.

Am I right?