Abstract

This paper gives a probabilistic analysis of a determinant D of order 2 and 3 in which the elements are i.i.d. Negative Binomial variates. Using Chebyshev’s ine-quality, fiducial limits (a type of statistical range used to estimate the uncertainty around a measured value) of D are obtained for order 2 and 3. The results may be compared with those obtained for other standard probability distributions. We are motivated to work in this problem considering the following applications: (1) Pre-dicting the area of a triangle whose vertices are random variables. (2) In solving optimization problems where the coefficients in the objective function or the con-straints are random variables. (3) Predicting the product of vectors (Cross Product) whose elements are random variables. (4) Predicting the equation of a plane con-taining two straight lines (in 3D) whose coefficients are random variables. (5) Pre-dicting the Eigen values and Eigen vectors for random square matrices. (6) Pre-dicting the solution of system of simultaneous linear equations, whose coefficients are random variables, using Cramer's rule.