Your friend asks how correlation is different from covariance, and for a formula that can turn $cov(x, y)$ into $cor(x, y)$. Provide that formula, and explain how correlation relates to covariance. Also explain what the correlation means and the possible values it can take.

See explanation below.

Explanation:

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

By definition the covariance "is a measure of the variability of two random variables". The covariance between x and y is defined as:

And we have the following relation between the covariance and the correlation coefficient:

So then we see that the correlation coeffcient is dependent of the covariance. If the covariance is + the r is + and if the covariance is - then r is negative, and the reasonis because if we see the last expression obtained the denominator can't be negative.  

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