Xn) from the Consider a random sample X: px n = (x1, X2, multivariate normal distribution,...

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Xn) from the Consider a random sample X: px n = (x1, X2, multivariate normal distribution, where the column vectors x; (of X) are independently and identically distributed as N₂(μ, Σ). Let 1/1X; and S X = i Σ(x₁ - x)(x₁ - x)' - n n-I a. Show that the sample mean (x) and the sample covariance matrix (S) are unbiased estimators of u and b. Show that x ~ N₁ (1, ²8) c. Show (n − 1)S is distributed as the Wishart random variable with parameters n − 1 and Σ, that is (n − 1)S ~ W₂(n − 1, Σ) d. Let W W₂(n, E). Show that E[W] = n. Xn) from the Consider a random sample X: px n = (x1, X2, multivariate normal distribution, where the column vectors x; (of X) are independently and identically distributed as N₂(μ, Σ). Let 1/1X; and S X = i Σ(x₁ - x)(x₁ - x)' - n n-I a. Show that the sample mean (x) and the sample covariance matrix (S) are unbiased estimators of u and b. Show that x ~ N₁ (1, ²8) c. Show (n − 1)S is distributed as the Wishart random variable with parameters n − 1 and Σ, that is (n − 1)S ~ W₂(n − 1, Σ) d. Let W W₂(n, E). Show that E[W] = n.