On a problem in probability theory

For continuous random variables, we study a problem similar to that considered earlier by one of the authors for discrete random variables. Let numbers N > 0, E > 0, 0 <= lambda(1) <= lambda(2) <=... <= lambda(s) be given. Consider a random vector x = (x(1),..., x(s),), uniformly distributed on the set xj >= 0, J = 1,...,s: Sigma(s)(j=1) xj = N, Sigma(s)(j=1)lambda(j)x(j) <= E. We study the weak limit of x as s -> infinity.