(Marginal normality and bivariate normality) Assume Y, Y2 ~iid N(0, 1). Consider the following two-dimensional vector:...

 

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(Marginal normality and bivariate normality) Assume Y₁, Y2 ~iid N(0, 1). Consider the following two-dimensional vector: (1.2), if Y₁ ≥0 (X1, X2) = { (Y₁,-2), if Y₁<0. Show that X1 and X2 are normally distributed, but that (X1, X2) does not follow a bivariate normal distribution. (Marginal normality and bivariate normality) Assume Y₁, Y2 ~iid N(0, 1). Consider the following two-dimensional vector: (1.2), if Y₁ ≥0 (X1, X2) = { (Y₁,-2), if Y₁<0. Show that X1 and X2 are normally distributed, but that (X1, X2) does not follow a bivariate normal distribution.