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)= ½ Y^2
(b) show that , for 1≤ Y≤ 2, P( X1 +X2 ≤ Y)=1- ½ (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?
Thanks a lot!