g Using the preceding exercises, and recalling the concept of the moment generator, show that if a set of N random variables {xi} are distributed according to a Gaussian distribution: 鈭欴etA (2 )N/2 e鈭 1 2 Pkl Aklxkxl , (4) - which, note, is normalized - the following is true: hxii = 0 (5) hxixji = (A鈭 j (6) What is the condition for two variables to be correlated? Suppose now that two random variables x and y are gaussianly distributed and it is known that hxi = hyi = 0, and hx2i = 2 x , hy2i = 2 y, and hxyi = 2 xy. Write out explicitly the joint probability distribution function p(x, y)