Answer: decrease.

The correlation between two random variables, \(R_i\) and \(R_j\), is defined as \(\rho(R_i, R_j) = \frac{\text{Cov}(R_i, R_j)}{\sigma(R_i) \sigma(R_j)}\), where \(\text{Cov}\) denotes the covariance and \(\sigma\) the standard deviation. Since the standard deviation of each variable is in the denominator of the correlation formula, an increase in the variance (and thus the standard deviation) of either variable will decrease the correlation, assuming the covariance remains the same. This makes option A the correct choice. Options B and C are incorrect because the correlation does not remain unchanged or increase under these conditions.

Author: LeetQuiz Editorial Team