Gaussian function solution of random questions in stats

6. The (normalized) Gaussian function is defined as -2 2 g(x) = e 202 where J_ g(x)dx = 1. Note that this implies that the "DC component" of its Fourier transform G(0) = 1. Prove that the Fourier transform is also a Gaussian function of the form G ( w) = e 2 Hint: Use the differentiation with respect to t, and multiplication properties of the Fourier transform, and then integrate both sides.Problem 1 Consider a Gaussian function in the form: (x) = Ae-012/2 (1) a) Normalize this function, i.e., find the normalization constant A. b) Show that this function is the eigenfunction of a one-dimensional harmonic oscillator. c) Determine the parameter o via the mass and angular frequency of the oscillator. d) Derive the energy corresponding to this eigenfunction.Q1. Find probability of sending n bits (= A) to get max 2 errors, If error probability is P.=B 104 Check your A and B values! Q2. If CDF, F, (x)= 1-e " U(x), draw and find P.(x>B| x