try this.. P(Y<=y)=P(max(X,1-X)<=y) = P(X<=y,1-X<=y)=P(1-y<=X<=y)
The question: Given that a random variable X is uniformly distributed on (-1,1) and Y=max(X, 1-X), find the CDF of Y.
I tried to solve as following:
First I found the CDF of X, then I tried to find the relation between the CDF of X and the CDF of Y.
Y=max(X, 1-X) means that for x<0.5 y=1-x, and for x>0.5 y=x
So F_{Y}(alpha)=P(Y<alpha) but here I have a problem: which Y should I use? (y=x or y=1-x or both in some complicated way)
I've been thinking this over and over, but I just CAN'T find the solution.
Can you please please help me?
Thanks!