Let X 1 ,X 2 , . . .,X n be a random sample from a distribution with pdf f(x; ) = exp{|x|} /2(1/),

Let X₁,X₂, . . .,X_n be a random sample from a distribution with pdf f(x; θ) = θ exp{−|x|θ} /2Γ(1/θ), −∞ < x < ∞, where θ > 0. Suppose Ω = {θ : θ = 1, 2}. Consider the hypotheses H₀ : θ = 2 (a normal distribution) versus H₁ : θ = 1 (a double exponential distribution). Show that the likelihood ratio test can be based on the statistic W = Σⁿ_i=1(X²_i− |X_i|).