Question

the conditional probability that X greater than equal to 6 given X> 3, is ?

Answer 1

Let X,Y∼N(0,1) where X and Y are independent. Find E[X|X>Y]."

I know that E[X|Y=y]=∫∞−∞xfX|Y(x,y)dx, but in this case one is conditioning on an inequality, and I don't know how to treat that