As it is the product of two different random variables.also in denominator there is product of standard deviation

As the range of correlation is 0 to 1(less to high degree correlation)

This is the correct formula to calculate Karl Pearson's correlation coefficient. It will take a value ranging from -1 to +1. Positive values of correlation coefficient indicate positive relationship between the two variables, while negative values are indicative of a negative relationship.

Because the correlation between two variables can be negative or positive or no relation

Only karl Pearson method shows relation between two variables and spearman correlation shows ordinal aspects of the variables

As correlation is zero, the variables are not related with each other

If it is so then the fraction part will be zero and when zero is subtracted from1 we will get 1.

By change of scale we mean that all values of X and y series are multiplied or divided by some constant.by change of origin we mean that a constant is subtracted from all values of x and y series if the scale and origin of X and y series are changed the value of r remain unchanged

In 1904, Charles Edward Spearman developed the formula to calculate coefficient of correlation of qualitative variables.

Because the two series can be related directly or Inversely.