Point P is the midpoint of a line segment AB whose length is 1. Let point T1 be a random point between points A and P, and point T2 be a random point between points A and B. The random variable Z is the length of the line segment T1T2. Find the distribution function of Z and its expected value.
My current progress:
I will define the length of line segment AT1 as X and AT2 as Y. Which leads to Z=|Y-X|.
So there are 2 cases:
1) X > Y
2) Y > X
Now using graphs I find the limits of Z.
(I'd include a graph but im not allowed because the lack of reputation)
For the first case(X > Y) I get the limits of Z as [0, 0.5], and for the second case(Y > X) I get the limits of Z as [0.5, 1].
The funtion for the first case is Y=X-Z, and for the second is Y=X+Z
Now comes the part where I need to define the limits of the mariginal distribution which I am currently stuck on.