Need clarification of rms width definition

Hi Folks,

I am trying to calculate the rms width in time and frequency domain of
some intensity function, for example a gaussian.
I'm a bit confused about the definition of an rms width. I've seen one
definition which says that the rms width is the variance
(sigma)^2=<t>^2 - <t^2> and another definition where it defined as the
second order moment, which is just <t^2>. Does anyone know which one
is the correct definition.

Thanks.

.

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