Problem: Using Matlab, generate a vector x of length 1,000,000 whose components are N (0, 1) random variables (use random command of Matlab). Using Table 7.2 in the textbook, quantize x using an 8-level optimal quantizer  and callthe quantized vector x (in you Matlab program call is xhat). Determine the error vector x = x - x (in Matlab, xtilde = x - xhat). Compute the square error distortion and find the probabilities of each of the 8 outputs of the quantizer and compute the entropy of xhat. In your solution, give a lasting of your Matlab program as well as the computed distortion, probabilities for each quantization level, and the entropy of the quantized source. Compare the value of the distortion and the entropy of the quantized source. Compare the value of the distortion and the entropy with the given in Table 7.2.