2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate
a) P(X<0.5, Y<0.5)
b) P(X<0.5)
c) P(Y<0.5)
Thanks~
a. $\displaystyle \int_{x = 0}^{x = 1/2}\int_{y = 0}^{y = x}2 \cdot (x+y)\; dy \; dx$
b. Same as above.
c. $\displaystyle \int_{y = 0}^{y = 1/2}\int_{x = y}^{x = 1}2 \cdot (x+y)\; dx \; dy$
In each case it helps to draw the required region of integration to get the integral terminals.