central limit theorem

[Seth O'Beeth <seth3116@gmail.com>]

Folks:

Please help with quick reference regarding central limit theorem.

It is my undrstanding that

 

If {x[i]} i=1,...,N are iid with bounded moments,

 

and 

y is a mlutivriate normal with vector of means E(y) and variance-covariance matrix S[n,n]

 

then the sums sum(x*y) = x[1]*y[1] + x[2]*y[2] + ...+ x[n] * y[n]

are asymtotically (n->inf) normal.

 

Is this statement correct?

If yes, then can anybody please provide me with reference on some kind of text book or paper or Internet resource?

 

thank you in advance

 

Seth O'Beeth

 

Statistical Consultant