If I compute the marginal f(Θ) as the integral of joint over x (from x=3 to x=11), the answer I get is 1/4. But this is not even a pdf since the area under the curve is not 1.
Samewise, the marginal f(x) is 1/2 but again this is not correct. Am I doing something wrong in the integral bounds?
Also, if the marginal f(X) is uniform that means that eg. x=3(that can happen only for θ=4) has the same probability to occur as x=7 (that can happen for θ=6, θ=7, θ=8). Does that make sense? I got confused in general..