Congratulations! You've been hired as a financial scientist in the Stock Chemistry Lab. Your mission

is to discover the correlation coefficient between two mysterious stocks, Stock X and Stock Y$.$

The lab has provided you with the following information: The covariance between Stock X and Stock

Y is $0\mathrm{.}004.$ The standard deviation of Stock X is $0\mathrm{.}08.$ The standard deviation of Stock Y is $0\mathrm{.}10.$

Now, let's conduct a financial experiment:

a$)$ Calculate the Correlation Coefficient

b$)$ Interpret the results:

a$.$ What does it mean if the correlation coefficient is positive?

b$.$ What does it mean if the correlation coefficient is negative?

c$.$ Would there be diversification benefits by combining these two assets in a portfolio?