4. [25 points] Suppose that an analog signal is modeled as a random variable X which is uniformly distributed in the interval [-4, 4]. The analog signal X is passed through an A/D (analog- to-digital) converter which essentially is a quantizer. Specifically, the output of the quantizer, figure below. denoted as another random variable Q(X) takes four values {-3, -1, +1, +3} as shown in the Q ( x ) (quantized output) + 3 +1 -4 -2 +2 +4 X -1 - 3 (a) Compute the PMF of Q (X). (b) Let Z = X - Q(X) denote the "quantization error" random variable, representing th difference between X and it's quantized version Q(X). Find the expected value of Z