You don't mean that are jointly normal random variables? If so, would be the mean vector and the covariance matrix. would be diagonal if and only if all the random variables were independent.
If X1,X2,...,Xk are NIDp(u,S), does this mean that:
1) in each of the vectors X1,...,Xk etc there are p variables (like height, weight etc)?
like X1 = (90,153,14,121)^T, where 90=weight, 153=height, 14=age, 121=IQ?
2) Doe the fact that X1,X2,...,Xk are NIDp(u,S) mean that the covariance matrix S measuring the covariance between the vectors would be : a) pxp, and b) only have entries on its diagonals, c) be measuring the covariance between the variables??
I think that the answer to all the questions i've asked is yes, but its just the notation which is confusing me! So i'd love some clarification