Statistics, Calculus

c) i) Using the fact that [ edx = vit, explain how we can verify that the density function for the normal distribution N O, is a valid density function. 21 ii) Show that if X - NO. , then E(X) =0. iii) Given that [ xedx = , , show that var(X) = . Let f: R2 - R be given by: 21 7(x-2pxy+y?) f(x, y) = 2n v(1 - p3) for -1