I know that maybe this issue can be pre-college, but hey, an apology in advance.

This is the problem:

"The random variable is defined on the interval [0,2]. It is known that:

calculate:."

then, i did this:

(i) .... I apply the Baye’s theorem:

on the other hand: cuz

(ii) in the case of :

…. I apply the Baye’s theorem:

on the other hand: cuz

(iii)

Note: notice the difference between and (uppercase and lowercase)

then I think I'm wrong from the foundation, we would appreciate if someone guide me in this problem, and another thing, is ?