Assume that you have independent random samples z1, z2, and z3 from a standard normal distribution and want to convert them to samples ε1, ε2, and

ε3 from a trivariate normal distribution using the Cholesky decomposition.

Derive three formulas expressing ε1, ε2, and ε3 in terms of z1, z2, and z3 and the three correlations that are needed to define the trivariate normal distribution.

AppendixLO1