| (of any random variable) the function that assigns to each number the probability that the random variable takes a value less than or equal to the given number. |
distribution function
mathematical expression that describes the probability that a system will take on a specific value or set of values. The classic examples are associated with games of chance. The binomial distribution gives the probabilities that heads will come up a times and tails na times (for 0an), when a fair coin is tossed n times. Many phenomena, such as the distribution of IQs, approximate the classic bell-shaped, or normal, curve (see normal distribution). The highest point on the curve indicates the most common or modal value, which in most cases will be close to the average (mean) for the population. A well-known example from physics is the Maxwell-Boltzmann distribution law, which specifies the probability that a molecule of gas will be found with velocity components u, v, and w in the x, y, and z directions. A distribution function may take into account as many variables as one chooses to include.
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