Cumulative Frequency?

A random variable X is uniformly distributed between 0 and 1. Two independent observations are made,X1 and X2. Take (X1,X2 ) as a point on the lines X1 X2 =Y in a cartesian plane. X1 X2 =Y is triangular.

(a) show that , for 0 Y 1, P( X1 X2 Y)= Y^2





(b) show that , for 1 Y 2, P( X1 X2 Y)=1- (2-Y)^2





I know that f(x)=1 for 0 x 1 since X is uniformly distributed. But how do I solve (a)?

Can anyone show me the solution for (a) only so that I could solve (b) myself?
Is Y defined to be the random variable X1 X2? What is Y2? P( X1 X2 =Y) makes no sense, you cannot have the probability of a random variable being equal to another random variable.



Please post the question exactly as it is writen from wherever you got it from.





Note: Yes, the random variable Y = X1 X2 does follow a triangular distribution. Its pdf is equal to y if , 2 - y if and zero otherwise.