Denote by *f(x _{i},y_{i}), f* is called the joint probability
distribution function of

The concept of independent events leads quite naturally to a similar definition for independent random variables.

Two random variables *X* and *Y* are said to be independent if

Roughly speaking, *X* and *Y* are independent if knowing the value of one does not
change the distribution of the other.

Thus, if *X* and *Y* are independent, then:

It follows that if *X* and *Y* are independent, then

Dependent variables may also be uncorrelated, if the relationship is non-linear, a u-curve for instance.

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