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 n−a times (for 0≤a≤n), 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.