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 $\displaystyle X_{1}, X_{2}, X_{3}, X_{4}, X_{5}$, the second question has 4 possible categories each of which has also a normal distribution, the corresponding random variables are $\displaystyle Y_{1}, Y_{2}, Y_{3}, Y_{4}$.

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