Normal Distribution Gauss file(s) basic_normal.g, basic_normal_like.g Matlab file(s) basic_normal.m, basic_normal_like.m A sample of T = 5 observations consisting of the values {1, 2, 5, 1, 2} is drawn from the normal distribution f(y; θ) = 1 √ 2πσ2 exp  − (y − µ) 2 2σ 2  , where θ = {µ, σ2}.

(a) Assume that σ 2 = 1. (i) Derive the log-likelihood function, lnLT (θ). (ii) Derive and interpret the maximum likelihood estimator, θb. (iii) Compute the maximum likelihood estimate, θb. (iv) Compute ln lt(θb), gt(θb) and ht(θb). (v) Compute ln LT (θb), GT (θb) and HT (θb).

(b) Repeat part

(a) for the case where both the mean and the variance are unknown, θ = {µ, σ2}.