For example, the probability density function of a random variable X may depend on a parameter . In that case, the function may be denoted to indicate the dependence on the parameter . is not a formal argument of the function as it is considered to be fixed. However, each different value of the parameter gives a different probability density function. Then the parametric family of densities is the set of functions , where denotes the set of all possible values that the parameter can take. In particular the normal distribution is actually a family of similarly shaped distributions parametrized by their mean and their variance.