Two random variables X and Y are distributed according to Fi

Two random variables, X and Y, are distributed according to Find K. What is the probability that X+ Y > 1 ? Find Pr(X> Y). What is Pr(X > Y|X+ 2Y > 1) ? Find Pr(X = Y). Find the marginal densities f_X(x) and f_Y(y).

Solution

a) k=1

b) 2/3

c) 1/2

d)5/12

e)0

f)f_x(x)=x+(1/2), f_y(y)=y+(1/2)