On random algebraic polynomials

This paper provides asymptotic estimates for the expected number of real ze ros and K-level crossings of a random algebraic polynomial of the form [GRAPHICS] where a(j)(j = 0,1,..., n-1) are independent standard normal random variabl es and K is a constant independent of x. It is shown that these asymptotic estimates are much greater than those for algebraic polynomials of the form a(0) + a(1) x + a(2)x(2) +...+ a(n-1)x(n-1).