Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 4, Pages 253-261
doi:10.1155/S1048953390000235
On the variance of the number of real roots of a random trigonometric polynomial
Department of Mathematical Statistics, University of Cape Town, Rondebosch 7700, South Africa
Received 1 July 1989; Revised 1 April 1990
Copyright © 1990 K. Farahmand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper provides an upper estimate for the variance of the number of real
zeros of the random trigonometric polynomial g1cosθ+g2cos2θ+…+gncosnθ. The coefficients gi(i=1,2,…,n) are assumed independent and
normally distributed with mean zero and variance one.