Let X₁,..., Xn be a random sample of size n > 1 from the N(μ, o²) distribution, where μ€ (-∞, +∞) and o² >0 are two unknown parameters. Since the value of o² depends on the value of μ, we cannot estimate o² without estimating and we cannot expect to estimate two unknown parameters unless we have at least two data points - hence the requirement that n > 1. Given a data sample (x₁,...,xn), the likelihood function of (μ, o²) is defined as n 1 ² 1 C(14,0³²) = (2705²) exp ( - 203² Σ(²; − µ)²). - i=1 You can freely use the fact that the random variable Σ(x − x)2 - i=1 has the x² distribution with (n − 1) degrees of freedom x= (a) Without using any tools from multivariable calculus, show that (x, s²), where W = n (b) Calculate E(S²), where n i=1 n 1 n ₁ and ²: = 1.n ·Σ(x₁ - x)², i=1 is the global maximizer of the likelihood function L. n (X; – X)² with X = 1 n n ΣX₁. i=1