A number of theories have been developed to describe the key position of the normal distribution as it applies to statistical and probabilistic problems. This paper investigates special properties of equidistributional contours, defined as a functional relationship between lower limits on the range of integration for the upper bivariate normal cumulative distribution with fixed value. Discussion covers both standard and nonstandard probability distributions. The statistical theorems presented are applicable to the formulation and numerical solution of stochastic optimization problems associated with water pollution control. 12 pp. Ref.
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