in [0, 180] is . Instead of speaking of a probability mass function, we say that the probability density of X is 1/360. The probability of a subset of [0, 360) can be calculated by multiplying the measure of the set by 1/360. In general, the probability of a set for a given continuous random variable can be calculated by integrating the density over the given set. More formally, given any interval , a random variable is called a "continuous uniform random variable" (CURV) if the probability that it takes a value in a subinterval depends only on the length of the subinterval. This implies that the probability of falling in any subinterval is proportional to the length of the subinterval, that is, if , one has where the last equality results from the unitarity axiom of probability. The probability density function of a CURV is given by the indicator function of its interval of support normalized by the interval's length: Of particular interest is the uniform distribution on the unit interval . Samples of any desired probability distribution can be generated by calculating the quantile function of on a randomly-generated number distributed uniformly on the unit interval. This exploits properties of cumulative distribution functions, which are a unifying framework for all random variables. Mixed type A mixed random variable is a random variable whose cumulative distribution function is neither discrete nor everywhere-continuous. It can be realized as a mixture of a discrete random variable and a continuous random variable; in which case the will be the weighted average of the CDFs of the component variables. An example of a random variable of mixed type would be based on an experiment where a coin is flipped and the spinner is spun only if the result of the coin toss is heads. If the result is tails, X = −1; otherwise X = the value of the spinner as in the preceding example. There is a probability of that this random variable will have the value −1. Other ranges of values would have half the probabilities of the last example. Most generally, every probability distribution on the real line is a mixture of discrete part, singular part, and an absolutely continuous part; see . The discrete part is concentrated on a countable set, but this set may be dense (like the set of all rational numbers). Measure-theoretic definition The most formal,