I have two questions, which a sample of people answer. Suppose the answer to the first question has 5 possible categories each of which has a normal distribution, the corresponding random variables are X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, the second question has 4 possible categories each of which has also a normal distribution, the corresponding random variables are Y_{1}, Y_{2}, Y_{3}, Y_{4}.

How can I estimate the correlation between each X_{i} and Y_{j}, i=1...5, j = 1...4?