(25 points.) A quantizer maps a random voltage X into a digital value q( X) from a set of representation values as shown in the figure below. We define the quantization error Y as the difference between X and its quantized value, i.e., Y = X - Q(X). Set d = 1 and assume that X has a uniform distribution over [-4, 4]. Find the distribution of Y. 7d Ad 2 Sd 2 d -4d -3d -2d -d q(x) 0 3d -d 0 d 2d 3d 4d 5d N -2d 2 7d -3d 2 -4d