I have a 2 by 1 variable u_t that varies across time t=1,....,T. This variable follows the multivariate normal N(0, (1\lambda_t)*Sigma) where lambda_t is a scalar , varies across time and follows a gamma density. Sigma is a 2 by 2 matrix.
I want to find the
where lambda=the vector of all lambda_t's
But the mvnpdf does not allow for that since this product (1\lambda)Sigma makes no sense. Is there a way of finding
mvnpdf(u_t(j,:),(1\lambda)Sigma) for each j?
Thanks is advance