Problem bank

Problem 271 of 333MediumProbabilityP271

Three correlated normals by hand

  1. Given independent standard normals Z1,Z2,Z3Z_1, Z_2, Z_3, construct X1,X2,X3X_1, X_2, X_3, each standard normal, with correlation matrix

    R=(10.60.480.610.80.480.81)R = \begin{pmatrix} 1 & 0.6 & 0.48 \\ 0.6 & 1 & 0.8 \\ 0.48 & 0.8 & 1 \end{pmatrix}

    Write each XiX_i explicitly as a combination of the ZjZ_j.