Question

(a) Show that (Xi, X2) has a bivariate normal distribution with means μ1 , μ2, variances 어 and 05, and correlation coefficient ρ if and only if every linear combination c Xc2X2 has a univariate normal distr bution with mean c1μι-c2μ2, and variance c?σ? + c3- +2c1c2ρσ12, where cı and c2 are real constants, not both equal to zero. (b) Let Yİ = Xi/ởi, i = 1,2. Show that Var(Y-Yo) = 2(1-2).

Answer 1