The joint probability density function f(x,y) is defined such that it equals xy when x and y are between 0 and 1, and equals 0 otherwise. This function describes a random variable with two components, x and y, that are dependent on each other (as the value is the product of x and y). The domain of the function is restricted to the range of x and y being greater than or equal to 0 and less than or equal to 1.