Say we have three stochastic variables defined as follows:
rho = NormalDistribution[rhom,sigmar]; beta = NormalDistribution[betam,sigmab]; alpha = NormalDistribution[alpham,sigmaa];
rho = NormalDistribution[rhom,sigmar];
beta = NormalDistribution[betam,sigmab];
alpha = NormalDistribution[alpham,sigmaa];
I would like to compute the central moments of the following vector containing functions of such variables:
ml={{rho/(Sqrt[1+Tan[alpha]^2+Tan[beta]^2]) Tan[alpha]},{rho/(Sqrt[1+Tan[alpha]^2+Tan[beta]^2])Tan[beta]},{rho/(Sqrt[1+Tan[alpha]^2+Tan[beta]^2])}};
ml={{rho/(Sqrt[1+Tan[alpha]^2+Tan[beta]^2]) Tan[alpha]},
{rho/(Sqrt[1+Tan[alpha]^2+Tan[beta]^2]) Tan[beta]},
{rho/(Sqrt[1+Tan[alpha]^2+Tan[beta]^2])}};
How can this task be fulfilled taking advantage of the definition of such DistributionDistribution
objects?