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 of facing up after a roll. Let the random variable Xi denote the number of rolls that result in side i facing up. 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.

- unanswered X1 and X2 are uncorrelated.X1 and X2 are positively correlated.X1 and X2 are negatively correlated.

Question

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 of facing up after a roll. Let the random variable Xi denote the number of rolls that result in side i facing up. 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.

- unanswered X1 and X2 are uncorrelated.X1 and X2 are positively correlated.X1 and X2 are negatively correlated.