Question

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.

          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.

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 X1, X2, X3 and X4 are i.i.d from
N2(μ, Σ), then (X1 + 2X2 + 3X3 + 4X4)
follows N2(10μ, 10Σ).
(iii) The partial correlation coefficient and
multiple correlation coefficient alway lies
between 0 and 1.
(iv) For a renewal function M(t), limt →∞(Mt)/(t) = (1)/(μ).
(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.

Added by Amparo A.

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