3. [A binary quantizer with Laplacian input] Suppose X has pdf fX(u) = e |u| 2 and Y = g(X) where g(u) = (sign(u)) = if u 0 if u < 0 for some positive constant . So Y is the output of a binary quantizer with input X. (a) Describe the pdf or pmf of Y. (b) Determine the mean square quantization error, E[(X Y ) 2 ]. Your answer should depend on . (Hint: R 0 u k e udu = k! for nonnegative integers k.) (c) Determine to minimize the mean square quantization error