Consider n independent rolls of a k-sided fair die with k 2: the sides of the die are labelled 1,2,..., k, and each side has probability 1/k. Let the random variable X, denote the number of rolls that result in side i. Thus, the random vector (X1,.. .. Xk) has a multinomial distribution. 1. Which of the following statements is correct?

Try to answer without doing any calculations

a. X1 and X2 are uncorrelated.
b. X1 and X2 are positively correlated
c. X and X2 are negatively correlated.