Consider a Gaussian function: f(x) = 1 O2 where is the mean (or expectation) value and is the standard deviation. (a) (10 points) Show that the function is normalized. (b) (10 points) Calculate . (c) (10 points) Calculate . (d) (10 points) Calculate ( )2 (e) (10 points) Use Matlab or Mathematica to plot f(x) for u-1 and a = 1. Include the plot (5 points) and the code (5 points) with your submission. 1 e 2 () (f) (10 points) Use Matlab or Mathematica to plot f(x) for -2 and a = 2. Include the plot (5 points) and the code (5 points) with your submission