1. The problem statement, all variables and given/known data Suppose X and Y are jointly continuous random variables with joint density function f(x,y)=6x^{2}y, 0<x<y, x+y<2 f(x,y)=0, otherwise Find P(X<1/2 | Y=1). 2. Relevant equations 3. The attempt at a solution By definition, P(X<1/2 | Y=1) 1/2 =∫ f_{X|Y}(x|y=1) dx -∞ My computations: Marginal density of Y: fY(y)=2y^4, 0<y<1 fY(y)=2y(2-y)^3, 1<y<2 Condition density of X given Y=y: Case 1: For given/fixed 0<y<1, f_{X|Y}(x|y)=3x^2 / y^3, 0<x<y Case 2: For given/fixed 1<y<2, f_{X|Y}(x|y)=3x^2 / (2-y)^3, 0<x<2-y I hope these are correct. Now P(X<1/2 | Y=1) is the troublesome case because we are given Y=1, which formula for f_{X|Y}(x|y) should I use? Thanks for any help!