1. Find the value of A required to normalize the Gaussian distribution P(x) = Ae^(-(x-x0)^2)/(2̃σ^2). Note that the limits of integration are from -∞ to +∞. 2. Compute the mean of the variable x for the Gaussian distribution P(x) = Ae^(-(x-x0)^2)/(2σ^2), where A is as determined in problem 1. Note that the limits of integration are from -∞ to +∞. 3. Compute the variance of the variable x for the Gaussian distribution P(x) = Ae^(-(x-x0)^2)/(2σ^2), where A is as determined in problem 1. Note that the limits of integration are from -∞ to +∞. 4. Show that variance(x) = <x^2> - (<x>)^2.