Show that the Fourier transform of a Gaussian function is also a Gaussian function. Note that a Gaussian function, g(x), is given as follows: g (x) = e-ax2, a 20 And the Fourier transform of a function, f(x), is given by F(f (x)} = F(w) = | f(x)e -jux dx 1-00 (Hint: Start by differentiating the integral formula of the Fourier transform of a Gaussian w.r.t w)3. Suppose the cumulative distribution function of the length (in millimeters) of computer cables is 0 (x s 1200) F(x)= 0.1x-120 (1200 1210) (a) Determine P (x