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

K. Farahmand

 Department of Mathematical Statistics, University of Cape Town, Rondebosch 7700, South Africa
Received 1 July 1989; Revised 1 April 1990

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.