WSS Ergodic Process with Power Spectrum
You can compute the power of the process from its power spectrum as well as from its PDF. Equating the two gives you a relation between the constants $A$ and $B$. More specifically you get

$$\int_{-B}^BG_x(f)df=\frac{1}{2A}\int_{-A}^Ax^2dx$$

If I'm not mistaken this should give $A=\sqrt{3B}$.