Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 4, Pages 253-261

On the variance of the number of real roots of a random trigonometric polynomial

K. Farahmand

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.


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.