Suppose that x' = [x1 x2 . . xn] has a multivariate normal distribution with mean μ' = [μ1 μ2 μn] and variance-covariance matrix Iσ^2 where I is an n x n identity matrix. The moment generating function of the distribution of x is Mx(t) = e^t'μ+(σ^2/2)t't. The distribution of x'x is a χ^2(n, 1/2μ'μ) with moment generating function Mx'x(t) = (1 - 2tσ^2)^-n/2 exp { t/(1 - 2tσ^2) μ'μ } (a) Prove that the distribution of (x - μ)/σ is N(0, I) (b) Prove that y = (x-μ)'(x-μ)/σ^2 has a central χ^2 distribution with n degrees of freedom