Answer

We need to evaluate \(f_{\Theta \vert X}(\theta \vert x)\) in order to get \(E[\Theta \vert X]\).

\(f_{X,\Theta}(x,\theta) = f_{X}(x) f_{\Theta \vert X}(\theta \vert x)\) which is a parallelogram on the \(\theta-x\) plane at the points \((3,4)\), \((5,4)\), \((9,10)\) and \((11,10)\). Then \(E[\Theta \vert X]\) can be obtained by drawing vertical lines on the planes and calculating the \(E[\theta]\) over that line. It is a line which bends at two points.