The Max quantizer Let X N(0, 2) (i.e., X takes on a normal distribution) and let the distortion measure be the squared error. Consider a one-bit Max quantizer for this Gaussian source. One bit is used to represent the RV X. If the RV is greater than or equal to 0, the value is represented by the digital ‘‘1’’. Otherwise, it is represented by the digital ‘‘0’’. The ‘‘1’’ and ‘‘0’’ correspond to two analog reproducer values used to produce the reconstruction ^ XðXÞ. Determine these two analog values such that the mean square error E½X  ^ XðXÞ2 is minimized. Also compute the expected distortion for this quantizer, and then compare this with the rate distortion limit.