Average Number of Level Crossings of a Random Algebraic Equation with Dependent Coefficients

Abstract

Let be a random algebraic polynomial of degree n, we have to find the number of level crossings of the polynomial where roots are identically distributed random variables with mean zero and variance one with joint density function constant particularly defined and a_i’s are non-zero numbers which are finite. It is shown that for any sequence of polynomials with dependent coefficient the number of level crossings for a positive constant n.