3. State whether the following statements are
true or false. Justify your answer with a short
proof or a counter-example:
10
(i) In correlation matrix R all off diagonal
elements are always positive.
(ii) If $X_1, X_2, X_3$ and $X_4$ are i.i.d from
$N_2(\mu, \Sigma)$, then ($X_1 + 2X_2 + 3X_3 + 4X_4$)
follows $N_2(10\mu, 10\Sigma)$.
(iii) The partial correlation coefficient and
multiple correlation coefficient alway lies
between 0 and 1.
(iv) For a renewal function $M(t)$, $\lim_{t \to \infty} \frac{M_t}{t} = \frac{1}{\mu}$.
(v) The general queuing system M/M/K/N
represents arrival follow Poisson process,
service times follow any general
distribution except Poisson or exponential,
multiserver queue with finite population.