NUMBER OF IAL ROOTS OF A RANDOM TRIGONOMETR2C POLYNOMIAL

We study the expected number of real roots of the random equation gl cosO + g2 cos20 +... + gn cosnO = K where the coefficients gj’s are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of gj, j = 1,2,...,n, it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients