The random vector x (XI, X2,... ,Xk)' is said to have a symmetric multivariate normal distribution...
The random vector x (XI, X2,... ,Xk)' is said to have a symmetric multivariate normal distribution if x ~ Ne(μ, Σ) where μ 1k, i.e., the mean of each X, is equal to the same constant μ, and Σ is the equicorre- lation dispersion matrix, i.e. when k 3, μ-0, σ2-2 and ρ 1/2, find the probability that Hint: Recall that if x = (Xi, , Xk), has a continuous symmetric dis tribution, then all possible permutations of X1,... ,Xk are equally likely, each having probability POG| 〈 < Xiv) = 1/k! for any permutation (il, . . . ,4) of the first k positive integers