It is possible to represent certain discrete random variables as well as random variables involving both a continuous and a discrete part with a generalized probability density function using the Dirac delta function. (This is not possible with a probability density function in the sense defined above, it may be done with a distribution.) For example, consider a binary discrete random variable having the Rademacher distribution —that is, taking −1 or 1 for values, with probability 1 ⁄ 2 each. The density of probability associated with this variable is: f ( t ) = 1 2 ( δ δ ( t + 1 ) + δ δ ( t − − 1 ) ) .