I have a Equation with following form: $$v(t)=e^{-( t/T_0 )^2}\sum_{n=-N}^{n=N}C_nCos(n\Omega t)$$ where $C_n $ is uniform random variable that take two integer 1 or -1 ,and $\Omega ,T_0, N $ are Constant, I want to calculate of rms width of this random process, and rms defined with following relation: $$T_\sigma=[<T^2>-<T>^2]^{1/2} $$ and $$<T^2>= {\int_{-\infty}^{\infty}t^n|v(t)|^2dt \over\int_{-\infty}^{\infty}|v(t)|^2dt} $$
Please Help me!