Probability distribution

A graph or equation depicting the probability that a randomly chosen member of a set will exist within a given range. Probability distributions are of two types: discrete and continuous. Discrete probability distributions are relatively easy to discern: a nonbiased coin can exist as heads or tails and therefore there is a 50% chance that either will appear after a flip. There is a 1/6 probability that a die will show any number between 1 and 6 when it is rolled since, if it unbiased, there is an equal chance than any of its six faces will appear. Continuous probability distributions depict the probability that a randomly chosen member of a set will exhibit a value within a particular range. Suppose, for example, that data were available for the height of 10,000 six-year-old children. A graph showing the number of children whose height was within one-inch intervals (between, say, 39 and 40 inches, 41 and 42, 42 and 43, and so on) was prepared. This graph would become a continuous probability distribution if each value were divided by the total population, in this case 10,000. Given this graph, the probability that a randomly chosen child would have a particular height could be estimated. Continuous probability distribution curves have names. The most important and frequently observed is the “normal" or Gaussian distribution. It is bell-shaped, peaking at some value (in the case of six year-olds, 42 inches) and tailing off on either side of this value. In futures research, a probability distribution curve might be used to show the number (or percentage of experts) who estimated the year of occurrence of some future event to be within a given future year. Many other curve shapes (equations) have been named and include: log normal distribution (in which the log of the intervals is normally distributed) and the Pareto distribution (a power law distribution in which the cumulative probability curve approaches the horizontal or vertical axis asymptotically).