<Dl> <Dd> f X (S) = min (S − 1, 13 − S) 36, for S ∈ (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) (\ displaystyle f_ (X) (S) = (\ frac (\ min (S - 1, 13 - S)) (36)), (\ text (for)) S \ in \ (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 \)) </Dd> </Dl> <Dd> f X (S) = min (S − 1, 13 − S) 36, for S ∈ (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) (\ displaystyle f_ (X) (S) = (\ frac (\ min (S - 1, 13 - S)) (36)), (\ text (for)) S \ in \ (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 \)) </Dd> <P> An example of a continuous random variable would be one based on a spinner that can choose a horizontal direction . Then the values taken by the random variable are directions . We could represent these directions by North, West, East, South, Southeast, etc . However, it is commonly more convenient to map the sample space to a random variable which takes values which are real numbers . This can be done, for example, by mapping a direction to a bearing in degrees clockwise from North . The random variable then takes values which are real numbers from the interval (0, 360), with all parts of the range being "equally likely". In this case, X = the angle spun . Any real number has probability zero of being selected, but a positive probability can be assigned to any range of values . For example, the probability of choosing a number 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 . </P> <P> 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 . </P>

Discrete random​ variable continuous random​ variable or not a random variable