1.19 For the multinomial distribution, show that

$$corr(n_j, n_k) = -\pi_j \pi_k/\sqrt{\pi_j (1 - \pi_j)\pi_k(1 - \pi_k)}.$$

When c = 2, show that this simplifies to corr(n1, n2) = -1, and explain why this makes intuitive sense.