Covariance

Suppose that X and Y are pair of random variables and they are dependent. We use covariance to measure the nature and strength of the relationship between them.

Definition:

Let X be a random variable with mean , and let Y be a random variable with mean .The expected value of is called the covariance between X and Y, denoted , defined as

.

An equivalent expression for is:

.

If is a positive, then there is a positive linear association between X and Y, if is a negative value, then there is a negative linear association between X and Y. An expectation of 0 for would imply an absence of linear association between X and Y.

Let us calculate for probability distribution shown in the

table 3.8.

Using an equivalent expression for yields:

It means that there is a weak negative association between number of tests taken a day during a final examination week and number of eaten snacks.

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