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The covariance between two variables is simply the average product of the values of two variables that have been expressed as deviations from their respective means. ------------------------------------------------------------------------------------------------- A worked example may be referenced at: http://math.info/Statistics/Covariance
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Why is covariance important?
Maybe I'm not providing a full information. But if you're asking about importance of covariance in trading, then before investing you should assess if your stocks are codependent. All investors try to diversify a portfolio and minimize risks. and covariance can show if two stocks are exposed to the same risk. Now it's easily calculated, there're different services. Actually, for better understanding just read Investopedia really.
Will the variance of the difference of two independent normally distributed random variables be equal to the SUM of the variances of the two distributions?
Yes it is. That is actually true for all random vars, assuming the covariance of the two random vars is zero (they are uncorrelated).
Where can one find information on the covariance matrix?
One can find information on the covariance matrix on the Wikipedia website where there is much information about the mathematics involved. One can also find information on Mathworks.
When do you use an F test?
When testing the sums of squares of variables which are independently identically distributed as normal variables. One of the main uses of the F-test is for testing for the significance of the Analysis of Variance (ANOVA) or of covariance.
Find the formula for percentage of covariance?
100 x (standard deviation/mean)
