The co-relation co-efficient of two random variable is defined as

The correlation coefficient of two random variables is a measure that determines the degree to which the pair of variables are linearly related. It is a value between -1 and 1 where:

1 indicates a strong positive relationship. -1 indicates a strong negative relationship. A result of zero indicates no relationship at all.

Here are the steps to calculate the correlation coefficient:

1. Find the mean (average) of the x-values (x̄) and the y-values (ȳ).
2. Subtract the mean of x from every x value (x-x̄), do the same for y (y-ȳ). This gives us "differences".
3. Square these "differences".
4. Multiply the "difference of x" and "difference of y" for each pair.
5. Sum all the values obtained from step 4.
6. Sum all the values obtained from step 3 for x and y separately.
7. Multiply the sums obtained from step 6.
8. Take the square root of the value obtained from step 7.
9. Divide the sum obtained from step 5 by the square root from step 8. This gives the correlation coefficient.

This is the formula for Pearson's correlation coefficient. There are other types of correlation coefficients as well, such as Spearman's rank correlation coefficient and Kendall's tau coefficient, which are used based on the type and distribution of data.